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Popular >

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

Solution

derivative of

f (t) = 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}

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Frequently Asked Questions (FAQ)

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