Find the most general f. f ''(x) = 5x + sin(x)

Q: Let y = 2 ln x - 1/2x then the first derivative is....., the first order condition is..... and the…

A: Given: y=2 ln x-12x To Find:  To determine the first order derivative.To determine the first order…

Q: Compute the derivative of the function y = 5 sin-'(x) at the point x = (Use symbolic notation and…

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Q: fla)=-sinx (): In, Cosx

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Q: Va2 -x2 y=Arcsin + 6. X

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Q: sin

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Q: Find the derivative of f(x) = tan³(sinx) + +

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Q: ind the derivative of f(x) = 2x/√x+1

A: Explanation:Given that  f(x)=2xx+1     Formula Used:fg'=f'g-fg'g2

Q: Find the second derivative of the function 2 f(x) = sin (3x). Show your work.

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Q: What is the derivative of 2(x)ln(x)+x

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Q: Find the first derivative of: y=〖sec〗^4 x-〖tan〗^4 x y=xArcsinx + √(1-x^2 )

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

Q: The derivative of sec2 2x(cos2x−sin2x) with respect to x is

A: Given: f(x)=sec2 2x(cos2x−sin2x)   Simplify the function before finding the derivative: By  the…

Q: What is the derivative of f(x)=3cos(x)+2sin(x) at the point x=−π

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Q: Find the derivative of each function by using an appropriate differentiation rule. 1) F(x)= sin(3…

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Q: 13. f(x) = e* In x

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Q: Find the derivative. Simplify where possible.

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Q: Find the derivative of: 3 sin (– 3x). Hint: sin (x) = [sin(x)]"...so use the chain rule (twice!).

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Q: What is the anti derivative of  f(x)= 2sin(x)-sec2(x)

A: Given information

Q: find the derivative oof 1/x^3 + 3* 1/square root of x

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Q: find the first derivative f'(x) at the point x 1.3. Use two point central difference

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Q: Find the 139th derivative of y=cos x а. Cos x b. Sin x С. -Cos x d. -Sin x

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Q: Find the derivative of (sinx)2(sin-1x)2

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Q: Use the sign of the derivative to establish the inequaltiy ln(1 + x) > x − x2 2 , ∀x >0

A: SOLUTION-

Q: 3. Find the derivative of f (x) tan (5x + 7), by first principle of differentiation

A: Given function is By first principle of differentiation, we have

Q: sinx 3. f(x)=(x)*

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Q: Find the derivative of the function. h(x) CoS x 6. %3D 1+ sin x sin x -61 coSX --6 cosx (1+ sin x)6…

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Q: What is f(2022) (cos x), the 2022nd derivative of f(x) = cos x? COS X sin a sina

A: To find 2022nd derivative of f(x) = cos(x).

Q: 2. Determine the derivative of f(x) = sin-'(2x)

A: Topic = Derivative

Q: Find the derivative of f(x)=(−x^3−6x^2−6x)sin(x).

A: See the attachment

Q: cos X sin x + cosX

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Q: Find the derivative of the function g(x) = (arctan x)³, first showing how to get the formula for -…

A: Consider the function  g(x)=tan−1x3

Q: find the first derivative of the function. F(x)= (1+sin2x/1-sin2x)^3

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Q: What is the derivative of 2x cos x ? 2 cos x - 2x sin x 2 cos x+ 2x sin x -2 sin x 2 sin x 2x-sin x

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Q: Find the first derivative of ƒ(x) = 7x¹⁰² cot(x). 10 f'(x) =

A: Given :fx=7x10excotx

Q: Find the derivative of f(x) = ln(2x^3 + x).

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Q: Find the derivative of:-6 sin(- 2x*). Hint: sin (x) [sin(x))*...so .so use the chain rule (twice!).

A: We will find the derivative of the given function.Below find the solution in the image.

Q: f(x)= sinx/cos x+1

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Q: Find the derivative of: sin sin(2x) sin sin(x) + cos (2x) cos(x) ans: -sinx solution?

A: We will use the formula cosA*cosB+sinA*sinB= cos(A-B) , with A=2x and B=x and simplify.

Q: 5. Find the derivative of --( 1 + sin 0 cos 0

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Q: Compute the derivative of the function y = 5 sin-'(x) at the point x (Use symbolic notation and…

A: We know, ddxsin-1(x)=11-x2

Q: Find the derivative of f(x)=(−x4−4x2−7x)sin(x).

A: d/dx (f(x)g(x))= f(x)g'(x)+g(x)f'(x)

Q: Find the derivative. f(x) = x sinh(x) - 4 cosh(x) f'(x) =

A: Given problem is :

Q: Find the first derivative of the function below: f(x) = arctan(sec(x ))

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Q: How would you find the 65th derivative of sin(x)? Is there a pattern that occurs that allows you to…

A: Let y = sinx.Compute the first derivative of y as follows.

Q: second order derivative of (5 sin 3x+cos^2 (3x )) is *

A: The function: y=5 sin3x+cos23x

Q: Find the derivative of the function f(x) = 6x2 - 6 cosx

A: the given function f(x)=6x2-6 cos x

Q: 5-cos x 3) f(x) = 5+sinx foo

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Q: 1. 1. f(x) = 4x³ · cos x

A: Given: fx=4x3.cosx

Q: Find the second derivative y=5e^x -2/x^3 +4sqrt(x) -12sec x + 5lnx - pi/2= Find equation of tangent…

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.