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Popular >

derivative of 5^{x^3}

Solution

derivative of

5^{x^{3}}

Solution

3 ln (5) \cdot 5^{x^{3}} x^{2}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{3} ln (5)) = 3 ln (5) x^{2}

= e^{x^{3} l n (5)} \cdot 3 ln (5) x^{2}

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

= 3 ln (5) \cdot 5^{x^{3}} x^{2}

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Frequently Asked Questions (FAQ)

What is the derivative of 5^{x^3} ?
The derivative of 5^{x^3} is 3ln(5)*5^{x^3}x^2
What is the first derivative of 5^{x^3} ?
The first derivative of 5^{x^3} is 3ln(5)*5^{x^3}x^2