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Popular Calculus >

derivative of f(x)=3^{(x^5)}

Solution

derivative of

f (x) = 3^{(x^{5})}

Solution

5 ln (3) \cdot 3^{x^{5}} x^{4}

Solution steps

\frac{d}{d x} (3^{x^{5}})

Apply exponent rule:

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

3^{x^{5}} = e^{x^{5} l n (3)}

= \frac{d}{d x} (e^{x^{5} l n (3)})

Apply the chain rule:

e^{x^{5} l n (3)} \frac{d}{d x} (x^{5} ln (3))

= e^{x^{5} l n (3)} \frac{d}{d x} (x^{5} ln (3))

\frac{d}{d x} (x^{5} ln (3)) = 5 ln (3) x^{4}

= e^{x^{5} l n (3)} \cdot 5 ln (3) x^{4}

e^{x^{5} l n (3)} = 3^{x^{5}}

= 5 ln (3) \cdot 3^{x^{5}} x^{4}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=3^{(x^5)} ?
The derivative of f(x)=3^{(x^5)} is 5ln(3)*3^{x^5}x^4
What is the first derivative of f(x)=3^{(x^5)} ?
The first derivative of f(x)=3^{(x^5)} is 5ln(3)*3^{x^5}x^4