What is (\partial)/(\partial x)(5^{x^2}) ?

The answer to (\partial)/(\partial x)(5^{x^2}) is 2ln(5)*5^{x^2}x

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(\partial)/(\partial x)(5^{x^2})

\frac{\partial}{\partial x} (5^{x^{2}})

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

Solution steps

\frac{\partial}{\partial x} (5^{x^{2}})

Apply exponent rule:

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

5^{x^{2}} = e^{x^{2} l n (5)}

= \frac{\partial}{\partial x} (e^{x^{2} l n (5)})

Apply the chain rule:

e^{x^{2} l n (5)} \frac{\partial}{\partial x} (x^{2} ln (5))

= e^{x^{2} l n (5)} \frac{\partial}{\partial x} (x^{2} ln (5))

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

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

e^{x^{2} l n (5)} = 5^{x^{2}}

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

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What is (\partial)/(\partial x)(5^{x^2}) ?
The answer to (\partial)/(\partial x)(5^{x^2}) is 2ln(5)*5^{x^2}x