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What is the derivative of #5^(x^2)#?

1 Answer

Nov 6, 2016

# d/dx5^(x^2) = (2ln 5)x5^(x^2) #

Explanation:

Let # y = 5^(x^2) #

Take Natural logs of both sides
# ln y = ln 5^(x^2) #
# :. ln y = x^2ln 5 #

Differentiate (implicitly) wrt #x#:
# :. 1/ydy/dx = 2xln 5 #
# :. dy/dx = (2ln 5)xy #
# :. dy/dx = (2ln 5)x5^(x^2) #

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