Evaluate y' if y = vtan x

Q: finf dy/dx by implicit differentiation when x^2=(3x+6y)/(3x-6y).

A: The given function is: x2=3x+6y3x-6y

Q: y = x*lnx %3D %3D

A:

Q: Explain the derivatives and integration.

A: Solution: Derivatives: Definition of derivatives is , the rate of change of a quantity with respect…

Q: Find the first four derivatives of y = 4sinx. %3D

A:

Q: Vt- 4 V3t - 4 y =

A:

Q: 5. Second derivative of y = 1+t)< t2

A: Given: y = 1+t2t2 To find: Second derivative of the given function.

Q: Use differentials to estimate the value. estimate =  exact value =

A:

Q: Explain how a directional derivative is formed from the two partial derivatives ƒx and ƒy.

A:

Q: Compute the derivative: 3 | Vsin t dt dx

A: To find ddx∫x3sin t dt We know that, ddx∫u(x)v(x)f(t) dt = f(v(x))v'(x)-f(u(x))u'(x) Then, we have,…

Q: Find the derivative of the function. y = 3x + V3 3x + V3x y' =

A:

Q: How can you relate antiderivatives as an opposite of derivatives in your life? explain

A: Solution is given below:

Q: Calculate the derivative: + (2t3 – 9t) dt = dz

A: Evaluate the given derivative as follows. ddx∫0x2t3-9tdt=ddx2t44-9t220x=ddx2x44-9x22-0

Q: y = = Vsin va

A:

Q: y = x* + 2 sin(x) + xº + 24*.

A:

Q: Differentiate: F(y) (y + 9y°) yA - y?

A:

Q: Obtain the derivative of the function y 4y sen (3x) – 7x In(2x + y) = e* - ey + 4tg(y)

A:

Q: 5 Calculate the second and the third derivative of y = 6x – y": y"

A:

Q: How can linear approximation be used to approximate the changein y = f(x) given a change in x?

A: Given;                 y=fx How can linear approximation be used to approximate the changein y=f(x)…

Q: Find the derivative of the function. y = ek tan(V 5x) y'(x)

A:

Q: Explain how to determine Partial derivatives for y-value ?

A: For a multi variable functions like f(x,y) To find its partial derivative for y value, treat x as a…

Q: what is the partial derivative of 2=Yytylnlxy

A: Given query is to find the partial derivatives.

Q: Calculate the second derivative y : Vx - /y = 1

A:

Q: Use central difference approximations to estimate the first and second derivatives of y = e* at x =…

A:

Q: Calculate the derivative. 1 y = log 5x y' =0

A:

Q: Integrate sec√x dx ÷ √x

A: We have to Integrate : ∫secxxdx Let x=t⇒12xdx=dt⇒dx=2xdt=2t dt Now, ∫secxxdx=∫sec tt(2t dt)=∫2 sec t…

Q: Find derivative of y=xsin2x

A: We will need product rule. Assume, u=x and v=sin2x. Now, we have u=x ⇒u'=dudx=dxdx=1  and v=sin2x…

Q: f(x, y)= xe"+x sin(xy)+x*y

A:

Q: Find the derivative. y = ecosh(8x) y'(x) =

A:

Q: Find the second derivative of y = (4 – 2x)2 + 2sinx. dy Directly type your answer WITHOUT y' or dx…

A:

Q: Differentiate the function. y = etan(8) y' =

A: The given function is y=etanθ.

Q: Find anti derivative 3x^2(y^2+1)

A:

Q: Find the derivative of the function. y = In(Icsc(7x)|) y'(x) =

A:

Q: Find both first partial derivatives. az

A:

Q: find fsubxz if (x, y, z) = ye^x + x ln z

A:

Q: Determine the second derivative of 2x+ y-- 4 y 6.x (y + 2)--9(y+2) A B - 6x (y+ 2)-+ (y + 2) - 6x (y…

A:

Q: Find the derivative of y: 1- y = (cos 0)V2 Cos O 2- y = 7sec ln 7 3- y = 2sin 3t

A:

Q: Find the derivative of: x²y = (y + 2) + ry sin(x)

A:

Q: Find all second order partial derivative with respect to variable x and y. F(х,у)- х сosxу + y sinx…

A:

Q: Find the first and second order derivative w=3z7-7z3+21z2

A:

Q: Find the derivative of y with respect to s. y= sec -1(9s5 + 5)

A: To find the derivative of  y=sec-1(9s⁵+5)

Q: What is the first-order derivative of y = x^y?

A:

Q: Determine the derivative of y. y = eV14x+6 %3D

A: Please refer the attached image for complete solution.

Q: Explain how to find a first partial derivative of a function oftwo variables.

A: To get the first partial derivative of a function z = f(x, y) with respect to x we have to…

Q: The derivative of y=esinh/x + coshVx equals Select one: 1 1 (esinh/cosh/x + Vx² -1 2х 1 O y' = e…

A: We have to solve

Q: Find dy ax oy Impticit dipTErentation 3. Find 2nd derivative

A: 1) The given equation is 2x2+2y2=17 Differentiate both sides of given equation 2x2+2y2=17 with…

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

A: Given: y=∫x22x2lnt dt

Q: Find the derivative car (x+y) = yrinx

A:

Q: Determine the second derivative of 6 y – xy²= I Ay"= 2y³ ( 6 – 2x y)-2 ( 2 - x y ( 6 – 2x y )-1) ®…

A: Let's find.

Q: y=

A:

Q: Find y" by implicit differentiation. 9x2 + y2 = 4 y" = %3D

A: