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Popular >

derivative of 2^{t^3}

Solution

derivative of

2^{t^{3}}

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

Popular Examples

derivative of (x^2-2x/(x^2+5x))

\frac{d}{d x} (\frac{x ^{2} - 2 x}{x ^{2} + 5 x})

integral of 1/(xsqrt(25x^2-1))

\int \frac{1}{x 25 x ^{2} - 1} d x

x^2(dy)/(dx)-ysqrt(x)=0

x^{2} \frac{d y}{d x} - y x = 0

sum from n=0 to infinity of e^{-2n}

n = 0 \sum \infty e^{- 2 n}

limit as x approaches-4-of sqrt(5x+20)-8

x \to - 4 - lim (5 x + 20 - 8)

Frequently Asked Questions (FAQ)

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