15) Hyperbolic sine (sinh) is defined by sinh x = e* - e* Use this to find the derivative of hyperbolic sine. What function is this?

Q: Find derivative of the following functions 1. y= sin^-1 2x^2 2. y= tan^-1 2x^2/5

A: Given 1. y=sin-1(2x2)2. y=tan-1(2x25)

Q: 3 (8) Consider the curve given by 23 + x?y+ y³ = 1 Use implicit differentiation to find the equation…

A:

Q: Find the first derivative of g(x) = 2 ln(x)tan(x*). 2 tan(4) g'(z) = | 82 sec²(4) In(z)+ X syntax…

A: We will solve the problem. The syntax error is ln(x4)  instead of 'CAPITAL i'. Refer to the final…

Q: 7. Find the derivatives of y = cos- (sin(2x)) (show work)

A: Using derivatives of composite function. Or Using trigonometric transformation.

Q: 2. Find the derivative. Simplify where possible. (b) у %3 tanh-1(г3)

A:

Q: Find y’ if y=cos(ln(x^2 +1)) y’(0)= Use implicit differentiation to find the equation of the tangent…

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Q: (In z) dr and P -(a") = a* In a, dr Also, recall fundamental differentiation formulas or rules, such…

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Q: We cannot find the derivative of composed functions. We can however, using some algebra, find the…

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Q: What do the limits lim h-->0 ((sin h)/h) and lim h-->0 ((cos h - 1)/h) have to do with the…

A: Show the expression for derivative of sinx0  as follows:

Q: Let f and g be two functions having continuous second derivative on the interval [a, b). Its given…

A:

Q: 1. If the first derivative is zero and the second derivative is positive, what can be concluded in…

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Q: ) Prove that tanh'x = tn/itx, X€ (-1,1) i) , Sinh 'x and tanh'x Find the derivative of coch'x

A: (1). We have to prove that:   tanh-1x=12ln1+x1-x

Q: Find the derivative of the trigonometric function.

A: The given function is y=31-sinx2cosx

Q: 6. Find 39th derivative of f(x) = sinh(x). A. sinh(x) B. cosh(x) C. – sinh(x) D. - cosh(x) None of…

A: Derivative of sinh(x) is Cosh(x) and  Derivative of Cosh(x) is Sinh(x).

Q: Find the second derivative of f (x) = 2 sin (3x). Enclose arguments of functions in parentheses. For…

A: Differentiate two times

Q: 1. Find the derivative of the following sin² x cos² x a)y + 1+cotx 1+tan x

A: We have to find derivative of given trigonometric term.

Q: e3x _e-3x Y = e3x +e-3x]

A:

Q: 83. Find the 50th derivative of y = cos 2x.

A:

Q: 3) (a) Let f(x) = -x²-x. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

A:

Q: Example 17: Find the derivative of function g (t) = tan (5 - sin 2t). Solution: %3D Notice here that…

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Q: 5. х: t2-1 :-1

A: second differentiation of parametric equation is

Q: 1-cos 4x Find the derivative of y sin 4x

A:

Q: Find the second derivative of f (x) = 9 sin (2æ). Enclose arguments of functions in parentheses. For…

A: Second derivative of f(x) is given below...

Q: ) Find the y’’ (second derivative) of the following in its simplified form. Do not skip the steps…

A: This is a problem of differentiation of the function. Based on the general formula we will solve the…

Q: Find the derivative of: -2 sin (2x"). Hint: sin (x) = [sin(x)]...so use the chain rule (twice Submit…

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Q: sin(2 x) + 2 Find the function whose derivative is e 2cos x

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Q: Find the first derivative of the following function: 1. y = sin (2x) - cos (2x)

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Q: 2 If f(x) find f'(3) and us it to find an equation of the tangent line to the curve y = at ズー1 ズ-1…

A: Given function is, fx=2x-1

Q: How do you find derivative of y=ln(5x^9+7x)^7/5 or ln(5 to the 9th power plus 7x)all to the 7/5…

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Q: F of X equals 3 sin X + cos 4X;(pi,1) Find the derivative and find the slope of the tangent line to…

A: Given:FX=3 sin X+cos 4X ; the point π,1

Q: Find the derivative of the function. y = square root of 1 - x2 − x cos−1(x)

A:

Q: sin x.cos x- 8- Find y' for y = In x 9- Use the definition of differentiation to find the first…

A: Given  y=sin x cos x2ln x and f(x)=3x2 We need to differentiate these functions wrt x. This can be…

Q: 1. Use logarithmic differentiation to find the derivative of the function. y = x4 cos(x) 2. Use…

A: Here we have to find the derivative of the given functions using logarithmic differenciation.

Q: how to find the derivative of 1-sec x

A:

Q: Find the first derivative of the function 3 cos x y = x? sin(2e*)- ex Show all the works clearly.…

A: The given function is y=x2sin2ex-3cosxex.

Q: EXAMPLE 1.2 The Derivative of the Log of an Absolute Value For any x for which tanx # 0, evaluate In…

A: Solution of the problem as follows

Q: 3. Find if y³ + 2xy - x² = cos x using implicit differentiation.

A:

Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 %3D dx b) EVALUATE THE DERIVATIVE FROM PART a AT…

A: Given: x4y3=-8

Q: How to find the anti derivative of sin(x)/cos^3(x)

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Q: The function f(x) whose derivative is sin x and whose graph passes through the point(0, 2)​

A: we have to find the function f(x) whose derivative is sinx and whose graph passes through the point…

Q: 1+sin 2 x Find the derivative of f(x) 2 cos3 x

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Q: Y = 2 Arccos ( 1 -) + v4x – x²

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Q: 1+sin 2x 1) Find the derivative of f(x) = 2 cos x

A: To find The derivative of given f(x)

Q: Use Leibniz’s Rule to find the derivatives of the functions

A: Use Leibniz’s Rule to find the derivatives of the functions

Q: Solve for the derivative of the Trigonometric Differentiation. 1. y = sin (5x) + 3x cos (5x) 2. y…

A: given y=sin5x+3cos5xdiffrentiate w.r.t. xdydx=ddxsin5x+3cos5xdydx=ddx(sin5x)+ddx(3cos5x)we know that…

Q: Find the derivative of a. (e(sin2x))/[In(cos2x)]2

A: We have to find out derivative

Q: Show that x + yx−1 = 1 and y = x − x2 define the same curve [except that (0, 0) is not a solution of…

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Q: 1. State the power rule. 2. For which values of n have we proved the power rule? 3. Based on your…

A: 1. The power rule of derivatives gives the following: For any real number n,      ddxxn=nxn-1

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.