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Popular >

derivative of 7^{x^4}

Solution

\frac{d}{d x} (7^{x^{4}})

Solution

4 ln (7) \cdot 7^{x^{4}} x^{3}

Solution steps

\frac{d}{d x} (7^{x^{4}})

Apply exponent rule:

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

7^{x^{4}} = e^{x^{4} l n (7)}

= \frac{d}{d x} (e^{x^{4} l n (7)})

Apply the chain rule:

e^{x^{4} l n (7)} \frac{d}{d x} (x^{4} ln (7))

= e^{x^{4} l n (7)} \frac{d}{d x} (x^{4} ln (7))

\frac{d}{d x} (x^{4} ln (7)) = 4 ln (7) x^{3}

= e^{x^{4} l n (7)} \cdot 4 ln (7) x^{3}

e^{x^{4} l n (7)} = 7^{x^{4}}

= 4 ln (7) \cdot 7^{x^{4}} x^{3}

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Frequently Asked Questions (FAQ)

What is the derivative of 7^{x^4} ?
The derivative of 7^{x^4} is 4ln(7)*7^{x^4}x^3
What is the first derivative of 7^{x^4} ?
The first derivative of 7^{x^4} is 4ln(7)*7^{x^4}x^3