Differentiate g(x) = 6/T · e². Answer: gʻ(x)

Q: Find dx2 by implicit differentiation, given x³ + y³ = 8. d?y dx2

A: Given that, We have to find the value of  For that simply follow the step given as below

Q: 3) Use logarithmic differentiation to find the derivative of the function a) y = Vxe&*x? + 1)"

A: Answer

Q: Find the derivative. y = e(lnx)2

A: dydx=ddx e(lnx)2        =e(lnx)2 ddx2(ln x)         =e(lnx)2 2x

Q: Find the derivative of the function. y = ln(2 − e5x)

A:

Q: Find the differential of the function. Y = e2x

A: Given function is  y= e2x

Q: Find the derivative of function.

A: To find the derivative of the given function                                                y=log…

Q: Find Dxy for y = sinh-'(x5)

A:

Q: Find the first derivative of y = (ln x)4

A: Given the  y = ( ln x)^4 We need to find the first derivative . Therefore differentiate to given…

Q: y = kx xe

A: y=xe-kxTo solve the derivative

Q: find the second derivative of y=ln(e^x+e^-x)

A: Given query is to find the second derivative of the expression.

Q: Find the derivative of the function.

A:

Q: Find the derivative of the function y = ln(9 – e-ª).

A:

Q: For y=ln2x, determine the equation of a tangent line parallel to 2x-3y+1=0

A: here we find the equation of a tangent which is parallel to 2x-3y+1=0. y=mx+c slope = m.

Q: Find the equilibria of the differential eq

A:

Q: Find the first derivative for y = e

A: Given function is, y=e

Q: ア=e y =,

A:

Q: d. y = ار نے

A:

Q: Find the second derivative of the function. 3root(x) + e^(6x)ln(x)

A:

Q: What is the derivative of y = ekx? For what values of k does this rule apply?

A: Given function is, y=ekx. The derivative of the given function is found as follows: dydx=ddxekx=kekx

Q: Find the derivative. y = e(ln x)2

A:

Q: What is the derivative of y = e2 +1, with respect to x?

A: Formula used

Q: Find the y 'values and differentials for?

A:

Q: Find dy/dx by implicit differentiation. x3 − 3x2y + 2xy2 = 12

A: Given: x3-3x2y+2xy2=12 for finding dydx we differentiate given expression

Q: Differentiate the following function.   y = ln(ex2/x)

A:

Q: Determine the first derivative of the ff. function y = Vxe2* cos x

A: Derivative of a function gives the tangent of the curve at a given point. Derivatives are used to…

Q: find the derivative of ln(3x^2+e^x)

A:

Q: dy Use implicit differentiation to find dx e + x² – y² = 10

A: Given implicit function is exy+x2-y2=10.

Q: Solve for the derivative of y = x(e*) %3D

A: Find your answer below

Q: Find the second derivative of the function.

A: Given the function: g(x)=x + ex  ln(x) We have to find the second derivative of the function. Let's…

Q: (d) y = xnz²

A:

Q: Find the indicated derivative. dz if z = In (x° + e4) dx dz dx

A: We can find the derivative as below

Q: Excrcise 10. Find the derivative d -7x * [" (t³ + 2) dt dx

A: Given,          ddxx∫57xt3+2dt

Q: Find dy/dx by implicit differentiation. x3 + 7x + 3xy - y5 = 25

A:

Q: (b) Find the derivative of y = log,(5x')+log, (sin.x)

A:

Q: dy Find dx if y = v5 – x2 ,by using definition .)باستخدام صيغة تعریف المشتقة) formula of derivative

A: Given y=5-x2We know that f'(x)=limh→0f(x+h)-f(x)h...(1)f(x+h)=5-x2-2hx-h2f(x)=5-x2Put all these…

Q: - In y = e' sin x

A: We have to find dy/dx of the above equation.

Q: The 2nd derivative of the function x = Ci cosot + C2 sin ot with respect to t is

A: Given function is

Q: (b). Find the second derivative. y=x²-5vx

A:

Q: The derivative of y=eSinh/x +cosh¬/x equals

A:

Q: dy Find dx if y = V5- x2 , by using definition .)باستخدام صيغة تعريف المشتقة( formula of derivative

A:

Q: j. y=5 ln (x² +4)

A:

Q: Find the derivative of F(x) = t°e' ln tdt.

A:

Q: Find the derivative of the function y, below. y = 2x(ln x + In 7) – 2x + V2 dy da

A:

Q: y = x'e**

A:

Q: Find the equation of the tangent line to the function f (x) = e*²-1 ln(x + 1) when x= 0.

A:

Q: w(x) %3D хе*

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

Q: Find the derivative y=ln(t2)-arctan(t/4) y'=?

A: Given, y=ln(t2)-arctan(t/4) y'=?

Q: b) y = cosh(2Vx+1)

A:

Q: find the derivative of y with respect to the givenindependent variable.

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: