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Calculating Derivative – A multiplication of a polynom and an exponential function – Exercise 6363

Exercise

Find the derivative of the following function:

f(x)=x^5\cdot 5^x

Final Answer


f'(x)=5x^4\cdot 5^x(1+x\ln 5)

Solution

f(x)=x^5\cdot 5^x

Using Derivative formulas and the multiplication rule in Derivative Rules, we get the derivative:

f'(x)=5x^4\cdot 5^x+x^5\cdot 5^x\ln 5=

One can simplify the derivative:

=5x^4\cdot 5^x(1+x\ln 5)

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