13. Evaluate: sin(x²) dx A) 2x cos(x2) B) 2x sin(x?) C) 2x cos 2x D)2x cos x 14. Find the derivative of y = e*. A) 2x 2xe*? B) C) D) 2e2x 2xe2x 15. Find the derivative of y = cot (7x) A) -csc?7x B) -cot27x C) -cot27xcsc²7x D) -3cot27xcsc27x

Q: The first derivative of y = cos(3x-8) is O a. - sin( 3x-8) O b. 3 sin( 3x-8) O. - 3xsin( 3x-8) O d.…

A: Given function is, y=cos3x-8.   It is differentiated as follows: dydx=ddxcos3x-8

Q: Differentiate y = sin (x 2)

A:

Q: b) Differentiate (i) (i) the following functions clearly showing your working y = cos (4x4) y =…

A: Let us differentiate the functions with respect to x in the next steps.

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: Differentiate y = (-6+sinx)/(x+cosx)

A:

Q: sin(2w)dw =

A:

Q: Evaluate sin dx

A:

Q: what is y' of y=sin-1(cos x)

A:

Q: (tan V) (sec V) b) Evaluate dx

A: Given integral: I=∫tan4(x)sec2(x)xdx

Q: 4. The 1" derivative of y : cotx a) xsec?x + tanx b) xsecx - tanx c) cot x + xcsc'x d) cot x - xcscx

A:

Q: sinx

A:

Q: Integrate f(cos x)e*+sin xdx B. e-sinx +C A. -et+sinx + C c. ettsinx + C D. e+sinx C

A: Note:∘ddx(sinx) = cosx ∘ddx(a) = 0                                         where a is constant∘∫etdt…

Q: 5. (a) 2e' sin? (b) e cos ?1

A:

Q: y = Secx ( sinx+ Cosx)

A: Given, y=secxsinx+cosx And we have to find the dydx.

Q: 1) Find the derivatives of the following functions: a) x³e b) sin(x³ + 2x) I c) 1+x²

A: We are authorized to answer three parts at a time, so we are answering the first three parts. Please…