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

The derivative of 4^{x^3} is 3ln(2)*2^{2x^3+1}x^2

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

The first derivative of 4^{x^3} is 3ln(2)*2^{2x^3+1}x^2

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derivative of

4^{x^{3}}

3 ln (2) \cdot 2^{2 x^{3} + 1} x^{2}

Solution steps

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

Apply exponent rule:

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

4^{x^{3}} = e^{x^{3} l n (4)}

= \frac{d}{d x} (e^{x^{3} l n (4)})

Apply the chain rule:

e^{x^{3} l n (4)} \frac{d}{d x} (x^{3} ln (4))

= e^{x^{3} l n (4)} \frac{d}{d x} (x^{3} ln (4))

\frac{d}{d x} (x^{3} ln (4)) = 6 ln (2) x^{2}

= e^{x^{3} l n (4)} \cdot 6 ln (2) x^{2}

Simplify

e^{x^{3} l n (4)} \cdot 6 ln (2) x^{2} : 3 ln (2) \cdot 2^{2 x^{3} + 1} x^{2}

= 3 ln (2) \cdot 2^{2 x^{3} + 1} x^{2}

\frac{d}{d x} (x coth (6 + x^{2}))

\int \frac{e ^{x}}{( x - 1 )} d x

y^{^{'}} = - \frac{π}{2} t (1 + y^{2})

\frac{d}{d x} (\frac{ln ( x + 1 )}{x + 1})

What is the derivative of 4^{x^3} ?
The derivative of 4^{x^3} is 3ln(2)*2^{2x^3+1}x^2
What is the first derivative of 4^{x^3} ?
The first derivative of 4^{x^3} is 3ln(2)*2^{2x^3+1}x^2