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Popular Calculus >

derivative of f(x)=2^{x^3}

Solution

derivative of

f (x) = 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}

Graph

Popular Examples

y = x^{x} + 1

slope of (-2,-1),(4,2)

s l o p e (- 2, - 1), (4, 2)

derivative of 3+2x

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

tangent of f(x)= x/(x-2),\at x=1

t an g e n t f (x) = \frac{x}{x - 2}, at x = 1

limit as x approaches 1 of arcsec(x)

x \to 1 lim (arcsec (x))

Frequently Asked Questions (FAQ)

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