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Popular Calculus >

derivative of 7^{x^3}

Solution

\frac{d}{d x} (7^{x^{3}})

Solution

3 ln (7) \cdot 7^{x^{3}} x^{2}

Solution steps

\frac{d}{d x} (7^{x^{3}})

Apply exponent rule:

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

7^{x^{3}} = e^{x^{3} l n (7)}

= \frac{d}{d x} (e^{x^{3} l n (7)})

Apply the chain rule:

e^{x^{3} l n (7)} \frac{d}{d x} (x^{3} ln (7))

= e^{x^{3} l n (7)} \frac{d}{d x} (x^{3} ln (7))

\frac{d}{d x} (x^{3} ln (7)) = 3 ln (7) x^{2}

= e^{x^{3} l n (7)} \cdot 3 ln (7) x^{2}

e^{x^{3} l n (7)} = 7^{x^{3}}

= 3 ln (7) \cdot 7^{x^{3}} x^{2}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 7^{x^3} ?
The derivative of 7^{x^3} is 3ln(7)*7^{x^3}x^2
What is the first derivative of 7^{x^3} ?
The first derivative of 7^{x^3} is 3ln(7)*7^{x^3}x^2