What is the derivative of f(x)=((5^{3x^7})/(8x^2))^4 ?

The derivative of f(x)=((5^{3x^7})/(8x^2))^4 is (244140625^{x^7}(21ln(5)x^7-2))/(1024x^9)

What is the first derivative of f(x)=((5^{3x^7})/(8x^2))^4 ?

The first derivative of f(x)=((5^{3x^7})/(8x^2))^4 is (244140625^{x^7}(21ln(5)x^7-2))/(1024x^9)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = (\frac{5 ^{3 x^{7}}}{8 x ^{2}})^{4}

\frac{24414062 5 ^{x^{7}} ( 21 ln ( 5 ) x ^{7} - 2 )}{1024 x ^{9}}

Solution steps

\frac{d}{d x} (\frac{5 ^{3 x^{7}}}{8 x ^{2}})^{4}

Apply the chain rule:

4 (\frac{5 ^{3 x^{7}}}{8 x ^{2}})^{3} \frac{d}{d x} (\frac{5 ^{3 x^{7}}}{8 x ^{2}})

= 4 (\frac{5 ^{3 x^{7}}}{8 x ^{2}})^{3} \frac{d}{d x} (\frac{5 ^{3 x^{7}}}{8 x ^{2}})

\frac{d}{d x} (\frac{5 ^{3 x^{7}}}{8 x ^{2}}) = \frac{12 5 ^{x^{7}} ( 21 ln ( 5 ) x ^{7} - 2 )}{8 x ^{3}}

= 4 (\frac{5 ^{3 x^{7}}}{8 x ^{2}})^{3} \frac{12 5 ^{x^{7}} ( 21 ln ( 5 ) x ^{7} - 2 )}{8 x ^{3}}

Simplify

4 (\frac{5 ^{3 x^{7}}}{8 x ^{2}})^{3} \frac{12 5 ^{x^{7}} ( 21 ln ( 5 ) x ^{7} - 2 )}{8 x ^{3}} : \frac{24414062 5 ^{x^{7}} ( 21 ln ( 5 ) x ^{7} - 2 )}{1024 x ^{9}}

= \frac{24414062 5 ^{x^{7}} ( 21 ln ( 5 ) x ^{7} - 2 )}{1024 x ^{9}}

\int \frac{x - 3}{x ^{2} - 12 x + 36} d x

n = 1 \sum \infty \frac{n}{n + 3}

f (x) = (2 + 4 x) (5 - 4 x), at x = 1

y = 2 x^{3} - 2 x^{2} - 2 x

\frac{d y}{d x} + \frac{y}{x} = x^{3}

What is the derivative of f(x)=((5^{3x^7})/(8x^2))^4 ?
The derivative of f(x)=((5^{3x^7})/(8x^2))^4 is (244140625^{x^7}(21ln(5)x^7-2))/(1024x^9)
What is the first derivative of f(x)=((5^{3x^7})/(8x^2))^4 ?
The first derivative of f(x)=((5^{3x^7})/(8x^2))^4 is (244140625^{x^7}(21ln(5)x^7-2))/(1024x^9)