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

limit as x approaches 0+of x^{(1/x)}

x \to 0 + lim (x^{(\frac{1}{x})})

limit as x approaches 1-of x+3

x \to 1 - lim (x + 3)

(dy)/(dt)+3y=13sin(2t),y(0)=6

\frac{d y}{d t} + 3 y = 13 sin (2 t), y (0) = 6

tangent of f(x)=x^4+7x^2-x,(1,7)tangent of

f (x) = x^{4} + 7 x^{2} - x, (1, 7)

integral from 0 to 3 of (x^3-x)

\int_{0}^{3} (x^{3} - x) d x

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