Answer to Question #346264 in Calculus for Elam Voyi

Question

Differentiate:

f(x)= (2x⁴+5x+2)

g(x)= 3x²√6x³+5x²+1

h(x)= 4x²/√x+7

Answer 1

a)

$f'(x)= 2(4x^3)+5(1)+0$

$=8x^3+5$

b)

$g'(x)=(3x^2)'\sqrt{6x^3+5x^2+1}$

$+3x^2(\sqrt{6x^3+5x^2+1})'$

$=6x\sqrt{6x^3+5x^2+1}$

$+\dfrac{3x^2}{2\sqrt{6x^3+5x^2+1}}(6x^3+5x^2+1)'$

$=6x\sqrt{6x^3+5x^2+1}$

$+\dfrac{3x^2(18x^2+10x)}{2\sqrt{6x^3+5x^2+1}}$

$=\dfrac{3x(12x^3+10x^2+2+9x^3+5x^2)}{\sqrt{6x^3+5x^2+1}}$

$=\dfrac{3x(21x^3+15x^2+2)}{\sqrt{6x^3+5x^2+1}}$

c)

$h'(x)=\dfrac{(4x^2)'\sqrt{x+7}-4x^2(\sqrt{x+7})'}{x+7}$

$=\dfrac{8x\sqrt{x+7}-4x^2(\dfrac{1}{2\sqrt{x+7}})}{x+7}$

$=\dfrac{8x^2+56x-2x^2}{(x+7)^{3/2}}$

$=\dfrac{6x^2+56x}{(x+7)^{3/2}}$