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Popular >

derivative of 2^{x^3}

Solution

derivative of

2^{x^{3}}

Solution

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

Solution steps

\frac{d}{d x} (2^{x^{3}})

Apply exponent rule:

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

2^{x^{3}} = e^{x^{3} l n (2)}

= \frac{d}{d x} (e^{x^{3} l n (2)})

Apply the chain rule:

e^{x^{3} l n (2)} \frac{d}{d x} (x^{3} ln (2))

= e^{x^{3} l n (2)} \frac{d}{d x} (x^{3} ln (2))

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

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

e^{x^{3} l n (2)} = 2^{x^{3}}

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

Popular Examples

integral of 3/4 x^2

\int \frac{3}{4} x^{2} d x

integral from 1 to 3 of x^2+1

\int_{1}^{3} x^{2} + 1 d x

integral of xe^{(1+x^2)}

\int x e^{(1 + x^{2})} d x

5x^2y^'=y^'+5xe^{-y}

5 x^{2} y^{^{'}} = y^{^{'}} + 5 x e^{- y}

(\partial)/(\partial x)(W*L*H(W,L,x))

\frac{\partial}{\partial x} (W \cdot L \cdot H (W, L, x))

Frequently Asked Questions (FAQ)

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