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

The derivative of y=(x^5+2)^2(x^4+4)^4 is 10x^4(x^5+2)(x^4+4)^4+16x^3(x^4+4)^3(x^5+2)^2

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

The first derivative of y=(x^5+2)^2(x^4+4)^4 is 10x^4(x^5+2)(x^4+4)^4+16x^3(x^4+4)^3(x^5+2)^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

10 x^{4} (x^{5} + 2) (x^{4} + 4)^{4} + 16 x^{3} (x^{4} + 4)^{3} (x^{5} + 2)^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((x^{5} + 2)^{2}) = 10 x^{4} (x^{5} + 2)

\frac{d}{d x} ((x^{4} + 4)^{4}) = 16 x^{3} (x^{4} + 4)^{3}

= 10 x^{4} (x^{5} + 2) (x^{4} + 4)^{4} + 16 x^{3} (x^{4} + 4)^{3} (x^{5} + 2)^{2}

n = 1 \sum \infty (- 1)^{n} sin (\frac{2}{n})

\frac{d}{d x} (6 x + 4)

\int_{1}^{3} 3 r^{4} ln (r) d r

d y - (y - 5)^{2} d x = 0

x^{2}, 2 x^{4}, - 1, 1

What is the derivative of y=(x^5+2)^2(x^4+4)^4 ?
The derivative of y=(x^5+2)^2(x^4+4)^4 is 10x^4(x^5+2)(x^4+4)^4+16x^3(x^4+4)^3(x^5+2)^2
What is the first derivative of y=(x^5+2)^2(x^4+4)^4 ?
The first derivative of y=(x^5+2)^2(x^4+4)^4 is 10x^4(x^5+2)(x^4+4)^4+16x^3(x^4+4)^3(x^5+2)^2