Calculate the derivatives of the following:

Question

(also please could you show the steps, i'm so confused)

a) y = sinx - cosx

b) f(x) = x^2 + cosx

c) y = sin(x^2)

d) f(x) = x^5 sin (2x^3)

e) y = cos (sinx)

f) f(x) = sin^2 x

Answer 1

a) y = sinx - cosx

b) f(x) = x^2 + cosx <---- you absolutely must know how to do this

c) y = sin(x^2) <---- you absolutely must know how to do this

d) f(x) = x^5 sin (2x^3) <--- product rule
firstline derivative:
f ' (x) = (5x^4)sin(2x^3) + 4x^4(6x^2)cos(2x^3)
= ....

e) y = cos (sinx)
dy/dx = -sin(sinx) ( cosx)

did you mean: y = (cosx)(sinx) ?? , that would need a simple product rule

f) f(x) = sin^2 x or (sinx)^2 <---- you absolutely must know how to do this

Answer 2

d) f(x) = x^5 sin (2x^3) <--- product rule and chain rule
f ' (x) = (5x^4)sin(2x^3) + x^5(6x^2)cos(2x^3)