Find the derivative of the function. Simplify and express the answer using positive exponents only. y = y'

Q: Find the derivative of a power function with the negative exponent y=x−n.

A: We will use the power rule:

Q: find the derivative y= (sinx)*

A:

Q: Find the derivative of the function. y = 6sin(πx)

A: Formula:

Q: Find the 3rd derivative of the function y=ex/x.

A:

Q: Find the derivative of the function.

A:

Q: z (y/)° = y

A:

Q: Find the derivative of the function. 12) y = 2 secó x

A:

Q: Find the derivative of the function f (x) = sin°(x) (),

A:

Q: Find the derivative of the function. y = −6 sin 3x4

A:

Q: Find the derivative of the function. Simplify and express the answer using positive exponents only.…

A:

Q: Find the derivative of the function. Express it using positive exponents only. y…

A: For power 3, use the power rule. Then use the chain rule

Q: Find the derivative of the function y=x2sinx.

A: Given: y=x2 sin x To determine: Derivative of the given function.

Q: Calculate the derivative of the following functions. y = csc ex

A: According to the question, we have to find the derivative of the function y=csc ex. The derivative…

Q: Calculate the derivative of the function y=1+cosxsinx.

A: Given: y=1+cosxsinx we know that for finding derivative of given function we need to use product…

Q: Find the derivative of y = 3x2 sin x.

A: Given: y=3x2sinx for finding derivative of given expression we will use product rule given below…

Q: Calculate the derivative of the function y=2√x+33√x.

A: Given function is y=2x+33x Power rule of differentiation states that: ddxxn=nxn-1 Differentiating…

Q: Find the derivative of the function. y = 2eVx

A: The chain rule for differentiation is given by ddxfgx=f'gx.ddxgx.

Q: Find the derivative of the function. 4 y=デ

A:

Q: Find the derivative of the function f(x) = 7x sin(4x).

A:

Q: Find the derivative of the function. Express the answer using positive exponents only. y = (x −…

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Q: Use the rules of differentiation to find the derivative of the function. y = -10 y' = %3D

A:

Q: Find the derivative of the function. Simplify and express the answer using positive exponents only.…

A:

Q: find the derivative of (2 + j)

A:

Q: Find the derivative of the function. 8 +- +/5 y= 4. dx %3D

A:

Q: .Find the derivative of the function: y =x² +8sin .

A: To find the derivative of y.

Q: ■ Find the derivative of the function. Simplify wherepossible.  y =  ( tan -1 x ) 2

A: y=tan-1x2

Q: Find the derivative of the function Зх + у Зx + y = Зх

A: Given function,

Q: y=x²

A: I have stated the used formula in the solution

Q: Find the derivative of the function.

A: The given function is y=x2-sin2x4

Q: Find the derivative of the function y = cosh−1(3x)

A:

Q: Find the nth order derivative of the square root y=√x.

A: Let's first calculate the nth order derivative of the power function y=xm where m is a real number.

Q: Find the derivative of the function. f(x) = ex - xe

A:

Q: Find the derivative of the function y 5sin(x)

A: Consider the given function

Q: Find the second derivative of the function given by the equation x+y=ex−y.

A: Using implicit differentiation and the chain rule we find y'

Q: Find the derivative of the function. Simplify wherepossible.

A: we have to find the derivative of the given function  y=xsin-1x+1-x2

Q: Find the derivative of the function. y = xV4 - x2 + arcsin

A:

Q: 6. y = vx sin-'(x)

A: we havey=x sin-1(x)

Q: Calculate the derivative of the function y=(x−1)(x−2)2 without using the product rule for the…

A: Consider the given function y = (x−1)(x−2)2. Simplify the given expression as follows.…

Q: Find the derivative of the equation. cos (x) y = x y' ||

A: Here we have to use logarithmic differentiation. According to product rule of differentiation,…

Q: Find the 42nd derivative of the function y=sin(x).

A:

Q: Find the 3rd derivative of the function y=exx.

A: Differentiating with respect to x, we get Again differentiating with respect to x, we get

Q: find the derivative of y=sin2(3x).

A:

Q: Find the derivative of the function. 12 X %3D

A:

Q: w(x) %3D хе*

A: To find the second derivative of function w(x)=xex

Q: Calculate the derivative of the cubic function y=x3.

A: ddxxn=n xn-1

Q: find the derivative of the following function: y=(sinx/3x)+(3x/sinx)

A: Given function is:Applying derivative with respect to x:Distributing the derivative over addition:

Q: Find the derivative of the power function y=xn.

A: y= xn To find the derivative of y

Q: Find the derivative of the function. (2x

A: In the given question, the fundamental theorem of calculus is applied. The fundamental theorem of…