What is (\partial)/(\partial x)(7^{x^2+1}) ?

The answer to (\partial)/(\partial x)(7^{x^2+1}) is 2ln(7)*7^{x^2+1}x

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(\partial)/(\partial x)(7^{x^2+1})

\frac{\partial}{\partial x} (7^{x^{2} + 1})

2 ln (7) \cdot 7^{x^{2} + 1} x

Solution steps

\frac{\partial}{\partial x} (7^{x^{2} + 1})

Apply exponent rule:

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

7^{x^{2} + 1} = e^{(x^{2} + 1) l n (7)}

= \frac{\partial}{\partial x} (e^{(x^{2} + 1) l n (7)})

Apply the chain rule:

e^{(x^{2} + 1) l n (7)} \frac{\partial}{\partial x} ((x^{2} + 1) ln (7))

= e^{(x^{2} + 1) l n (7)} \frac{\partial}{\partial x} ((x^{2} + 1) ln (7))

\frac{\partial}{\partial x} ((x^{2} + 1) ln (7)) = 2 ln (7) x

= e^{(x^{2} + 1) l n (7)} \cdot 2 ln (7) x

e^{(x^{2} + 1) l n (7)} = 7^{x^{2} + 1}

= 2 ln (7) \cdot 7^{x^{2} + 1} x

x x x

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What is (\partial)/(\partial x)(7^{x^2+1}) ?
The answer to (\partial)/(\partial x)(7^{x^2+1}) is 2ln(7)*7^{x^2+1}x