# Calculus Derivative Homework help 10 points!!?

f(x)=4x^7-3x^5+4x^4-x^3+root 3

g(t)=4t^(2)-3t^(-2)+6

z=2root(t)-4sin(t)

h(x)=(3x-5)(4x^2+2)

y=2x^2-5/(2x^2-3x+3)

y=3x^3e^x

asked Oct 6, 2014 in CALCULUS

The function f(x) = 4x7 - 3x5 + 4x4 - x3 + √3

Apply dervative on each side with respect of x.

Apply the formulae d/dx( xn ) = nxn -1

d/dx(constant) = 0

f ' (x) = 28x6  - 15x4  + 16x3  - 3x2 + 0

f ' (x) = 28x6  - 15x4  + 16x3  - 3x2

The function g(t) = 4t2  - 3t-2  + 6

Apply dervative on each side with respect of t.

g'(t) = 8t + 6t-3

The function z = 2√t - 4sin(t)

Apply the formula d/dx (√x) = 1/(2√x)

d/dx(sinx) = cosx

z' = 2[1/(2√t)] - 4cos(t)]

z' = 1/√t - 4cos(t)

The function h(x) = (3x - 5) (4x2 + 2)

Apply derivative on each side with respect of x.

Apply product rule in derivatives d/dx(uv) = uv' + vu'.

u = 3x - 5, v = 4x2 + 2

u' = 3, v' = 8x

h'(x) = (3x - 5)(8x) + (4x2 + 2)(3)

= 24x2 - 40x + 12x2 + 6

h'(x) = 36x- 40x + 6.

The function y = (2x2 - 5)/ (2x2 - 3x + 3)

Apply derivative on each side with respect of x.

Apply quotient rule in derivatives d/dx(u/v) = [vu' - uv']/v2 .

u = 2x2 - 5, v = 2x2 - 3x + 3

u' = 4x , v' = 4x - 3

y' = [ (2x2 - 3x + 3)(4x) - (2x2 - 5)(4x - 3)]/(2x2 - 3x + 3)2

y' = [ 8x3 - 12x2 + 12x - 8x3 + 20x + 6x2 - 15]/(2x2 - 3x + 3)2

y' = [ - 6x2 + 32x - 15 ]/(2x2 - 3x + 3)2.

The function y = 3x3 ex

Apply dervative on each side with respect of x.

Apply product rule in derivatives d/dx(uv) = uv' + vu'.

u = 3x3 , v = ex

u' = 9x2 v' = ex

y' = (3x3)(ex) + (ex)(9x2)

y' = 3x2ex [ x + 3 ].