en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=3^{(x^5)}

Solution

derivative of

f (x) = 3^{(x^{5})}

Solution

5 ln (3) \cdot 3^{x^{5}} x^{4}

Solution steps

\frac{d}{d x} (3^{x^{5}})

Apply exponent rule:

a^{b} = e^{b l n (a)}

3^{x^{5}} = e^{x^{5} l n (3)}

= \frac{d}{d x} (e^{x^{5} l n (3)})

Apply the chain rule:

e^{x^{5} l n (3)} \frac{d}{d x} (x^{5} ln (3))

= e^{x^{5} l n (3)} \frac{d}{d x} (x^{5} ln (3))

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

= e^{x^{5} l n (3)} \cdot 5 ln (3) x^{4}

e^{x^{5} l n (3)} = 3^{x^{5}}

= 5 ln (3) \cdot 3^{x^{5}} x^{4}

Popular Examples

y^{^{'}} + b y = 0

integral of (x^2)/(sqrt((2-x^2)))

\int \frac{x ^{2}}{( 2 - x ^{2} )} d x

integral of sinh(10x)

\int sinh (10 x) d x

(x)^2y^{''}+3(x)y^'-3y=(x)^3

(x)^{2} y^{^{''}} + 3 (x) y^{^{'}} - 3 y = (x)^{3}

derivative of 1/(t^2)derivative of

\frac{1}{t ^{2}}

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=3^{(x^5)} ?
The derivative of f(x)=3^{(x^5)} is 5ln(3)*3^{x^5}x^4
What is the first derivative of f(x)=3^{(x^5)} ?
The first derivative of f(x)=3^{(x^5)} is 5ln(3)*3^{x^5}x^4