4- Find dy/dx for y = 3[(sin-"(e-3x*)²

Q: 2. (In(x)) ? dx Xる

A:

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

A:

Q: 11. Find e*sinx dx

A:

Q: find Dxy if y=e^(-2/x^2) Dxy=?

A:

Q: d Verify tanh - = X 1- x2 dx

A: Inverse hyperbolic tangent function can be expressed in logarithm funtion. Write tanh-1x=12ln1+x1-x…

Q: find (d^(2)y)/(dx^(2)). y=xcos(5x)-sin^(2)x

A: y=xcos5x-sin2x Differentiating with respect to x, we get…

Q: x* + 4 dx : %3D 3

A:

Q: (x^2 -1) dy/dx +2xy =x

A:

Q: Find dy/dx: a. 3x? – (xy²)/2 = 2y³ b. y = (cosx – nx)^**

A:

Q: -sech? (In 3.x)

A: We can find the answer as below.

Q: 8. f sec² (3x - 1) dx

A:

Q: (7) Find if \.Y =ln12- Cosx) , 2- Y= %3D

A: Calculate dydx. 1. y=ln 2-cos x. Derivate with respect to x by applying chain rule: dydx=dydududx.…

Q: dx 3 -1 (4-x²)7

A:

Q: Evaluate les-). d 3x dx OA (3x³- x?)e3x²-x?-1 O A. ² – x² – 1 OB. O B, e oc (9x² - 2x)e³x³-x? OC.…

A:

Q: 6. (D² + 1)y = 10e* sin x

A: see below the answer and explanation

Q: Find (d^(2)y)/dx^2 if y=sin(x)cos(x)

A:

Q: Find dy/dx for the equation xy^2+x=1

A: Given equation is

Q: Compute d dx -(xe).

A:

Q: dy/dx for (ln(tan(2x)-sqrt(3+e^2x) / (pi(x)^3-cos^2(-5x))

A: Given,     y  =  ln(tan2x)-3+e2xπx3-cos2(-5x)

Q: 1 sec"' x) = dx d (sec" x) -1

A:

Q: (4 - x2)3/2 dx 3

A: Consider, I=423∫-22(4-x2)3/2dx I =4232∫02(4-x2)3/2 dx   since f(x) is even function that is…