f). S(e} = In(sec8 + tan 8)

Q: Find the derivative using the formula f'(x)= g'h + gh' 1. cos x cot x Let g= cos x, and h= tan x.…

A:

Q: f(x) = sin (eX)

A:

Q: Find the derivative of the trigonometric function.

A: Given :           h(x) = sin 2x cos 2x   To find h'(x)

Q: x) = (5 + 2 sin x)²

A:

Q: Find the derivative of the following. y = -1/3tan3 x - sin2(2x)/tan x - cos2(2x) cot x +4

A: Differentiation of the function can be found with the help of the differentiation formula.…

Q: Compute the derivative of the following function and find its tangent line at x = 0. Graph the…

A:

Q: find the derivative using the appropriate rule or combination of rules. y = (cos 6x + sin x2)1/2

A: We have to find the derivative of the function: y=cos 6x+sin x212 We know the formula of…

Q: Find the derivative and simply. 1+cosx (a) f(x) = 1-cosx (b) f(x) = 3x5 cot-1 x

A: Part aGiven,          fx=1+cosx1-cosx

Q: Find. the derivative of tan(x)). with respect to X 1- y3=

A: Explanation of the answer is as follows

Q: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

A: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

Q: compute the derivative. f (θ) = eθ (5 sin θ − 4 tan θ)

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Q: Find the derivative of the following fuction.  f(x)=[(1+sinx)/(1+cosx)]1/2.

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Q: 1. sin(x + y) = xy² – 2x3

A: Given- sinx+y=xy2-2x3 To find- The derivative of the above expression using the implict…

Q: compute the derivative. y = tan(cos x)

A: A function is a relation between an input variable and an output variable wherein each input…

Q: find the derivative of y with respect to the appropriatevariable. = sin-1 (1 - t)

A: Given Trigonometric Expression: sin-11-t We can differentiate this trigonometric function with the…

Q: Use the rules of differentiation to find the derivative of the function

A: Given fθ=3cosθ-sinθ4

Q: Find the derivative of y with respect to x. 1 y = cot 16x² - 1 + sec - 1 2 - 1 4x, 4

A:

Q: Find the derivatives of the function defined as follows.

A: Given: y=ln|sinx2| To find dydx

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

A: Differentiate two times

Q: Find the derivatives of the function defined as follows.

A:

Q: What is the derivative of sin? x f(x) = with respect to x? COs x

A:

Q: Determine the derivative of the following functions with respect to the independent variables: .1 y…

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Q: f(x) = @tann + In (sec x) - ex at x = T

A: We know that general formula of derivatives is -  d(lnx)/dx = 1/x ; d(tanx)/dx= sec2x d(secx)/dx =…

Q: Find the derivative of the given function f(0) = sin' 0 3

A:

Q: Find the derivative. Simplify where possible. g(x)  =Cos h(In x)

A: The function is g(x)=cosh (ln x). We have ddxcoshx=sinhx. To find the derivative, apply the chain…

Q: Find the derivative of r = In (cos" x).

A:

Q: Find the derivative of g(t) = tan(5 - sin 2t).

A: Given function is gt=tan5-sin2t. To find the derivative of the function. Solution: Chain rule of…

Q: What is the Derivative of the following function;  y = Arctan 2(x 3)

A: To find: The derivative of y=tan-1x32. Formula used: Chain rule of derivative: fgx'=f'gx·gx Power…

Q: Find the derivative of the following functions using the long method (limits) y= tan x

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: F(x) = sin x + 2 cosx- 5

A: Fx=sinx+2cosx-5

Q: Find the derivative of the function. y = cot 2 ( sin x)

A:

Q: f(x) = sin° (tan(5e2*))

A: We can find the derivative as below using chain rule.

Q: f(x) = 2 cos I - 3:

A: Of a function y = f(x) of a variable x is a measure of the rate at which the value y of the function…

Q: Find the derivative of the following. y = x2 sin x + 2x cos x - sin x

A: We need to find the derivative of the following, y=x2sinx+2xcosx-sinx

Q: Find the first derivative of the followin the result whenever possible. V4 – x² 1.y = x arcsin=-

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: f(x) = cos vx

A: The derivative is defined as f'(x)=limh→0f(x+h)-f(x)h.

Q: Find the derivative of the following. y = 1/2 tan x sin (2x) + cos (2x)

A: Given function is y=12tanx sin2x+cos2x. Solution: Product rule of differentiation states that:…

Q: Find the derivative of  f(x) = tan(cos(x^2))

A: f'(x) = d (tan(cos x2)dx  f'(x) = sec2(cos(x2))d cos x2dx               because   d (tan(x))dx =…

Q: f(x) = (x + 6 sin x) (1 – 5 cos x -

A: To find the derivative of:f(x)=x+6sinx1-5cosx

Q: FIND THE DERIVATIVE Of THE GIveM. FUMCTIC 3.) f(x) = Logio( ) %3D 8.) g= arccose-* 9.): y = qsin? x…

A: To find the derivative of the function7) fx=log10xx-18) y=arccosec-x9)y=9sin2x

Q: Use the theorems on derivatives to find the derivative of the following function:   y = (cos(x))2 +…

A:

Q: Find the derivative of the fx and evaluate the derivative at the given value of a. f(x)=(sin…

A: Given that, f(x) = (sinx) ln(10x) a = π2 We have to find the derivative of f(x) at point a.

Q: Find the derivative using the appropriate rule or combination of rules. y = (cos 6x + sin x2)1/2

A:

Q: Find the derivative of the following function, where x is already declared as a symbolic variable: f…

A: We have to find the derivative of the given function…

Q: Derive the formula for the derivative with respect to x of cot x.

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Q: Find the derivative of the following function. g(x)= 1+cos x / x + sin x

A:

Q: Use the rules of differentiation to find the derivative of the function                     g( ) = 4…

A: g(x) = 4cosx +6 dg(x)dx = d(4cosx+6)dx             = d(4cosx)dx + d6dx…

Q: Find the first derivative of the function below: f(#) = cosh(cot(z² – 2x – 7)) %3D

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: