What is the derivative of (3x^{4x}) ?

The derivative of (3x^{4x}) is 4ln(3)*81^xx^{4x}+4x^{4x}(ln(x)+1)*81^x

What is the first derivative of (3x^{4x}) ?

The first derivative of (3x^{4x}) is 4ln(3)*81^xx^{4x}+4x^{4x}(ln(x)+1)*81^x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} ((3 x)^{4 x})

4 ln (3) \cdot 8 1^{x} x^{4 x} + 4 x^{4 x} (ln (x) + 1) \cdot 8 1^{x}

Solution steps

\frac{d}{d x} ((3 x)^{4 x})

Simplify

(3 x)^{4 x} : 8 1^{x} x^{4 x}

= \frac{d}{d x} (8 1^{x} x^{4 x})

Apply the Product Rule:

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

f = 8 1^{x}, g = x^{4 x}

= \frac{d}{d x} (8 1^{x}) x^{4 x} + \frac{d}{d x} (x^{4 x}) 8 1^{x}

\frac{d}{d x} (8 1^{x}) = 4 ln (3) \cdot 8 1^{x}

\frac{d}{d x} (x^{4 x}) = 4 x^{4 x} (ln (x) + 1)

= 4 ln (3) \cdot 8 1^{x} x^{4 x} + 4 x^{4 x} (ln (x) + 1) \cdot 8 1^{x}

\frac{d}{d x} (c x^{- 7})

\frac{d y}{d x} = \frac{sec ( y )}{( x + 2 ) ^{2}}

\int \frac{k}{x ^{4}} d x

\frac{\partial}{\partial y} (2 x - 4 y)

\int \frac{4 x ^{2} + 3}{0.4 x ^{3} + 0.9 x} d x

What is the derivative of (3x^{4x}) ?
The derivative of (3x^{4x}) is 4ln(3)*81^xx^{4x}+4x^{4x}(ln(x)+1)*81^x
What is the first derivative of (3x^{4x}) ?
The first derivative of (3x^{4x}) is 4ln(3)*81^xx^{4x}+4x^{4x}(ln(x)+1)*81^x