What is the derivative of y=(3x^2+4)(3+x^3)^5 ?

The derivative of y=(3x^2+4)(3+x^3)^5 is 6x(3+x^3)^5+15x^2(3+x^3)^4(3x^2+4)

What is the first derivative of y=(3x^2+4)(3+x^3)^5 ?

The first derivative of y=(3x^2+4)(3+x^3)^5 is 6x(3+x^3)^5+15x^2(3+x^3)^4(3x^2+4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = (3 x^{2} + 4) (3 + x^{3})^{5}

6 x (3 + x^{3})^{5} + 15 x^{2} (3 + x^{3})^{4} (3 x^{2} + 4)

Solution steps

\frac{d}{d x} ((3 x^{2} + 4) (3 + x^{3})^{5})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 3 x^{2} + 4, g = (3 + x^{3})^{5}

= \frac{d}{d x} (3 x^{2} + 4) (3 + x^{3})^{5} + \frac{d}{d x} ((3 + x^{3})^{5}) (3 x^{2} + 4)

\frac{d}{d x} (3 x^{2} + 4) = 6 x

\frac{d}{d x} ((3 + x^{3})^{5}) = 15 x^{2} (3 + x^{3})^{4}

= 6 x (3 + x^{3})^{5} + 15 x^{2} (3 + x^{3})^{4} (3 x^{2} + 4)

17 x, x^{2}

e^{x^{3} + 10 x}

\int \frac{ln ( 9 x )}{x} d x

\frac{d ^{3}}{d x ^{3}} (x (2 x + 1)^{3})

What is the derivative of y=(3x^2+4)(3+x^3)^5 ?
The derivative of y=(3x^2+4)(3+x^3)^5 is 6x(3+x^3)^5+15x^2(3+x^3)^4(3x^2+4)
What is the first derivative of y=(3x^2+4)(3+x^3)^5 ?
The first derivative of y=(3x^2+4)(3+x^3)^5 is 6x(3+x^3)^5+15x^2(3+x^3)^4(3x^2+4)