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)

Have a question? Found a mistake? – Write a comment below!
Was it helpful? You can buy me a cup of coffee here, which will make me very happy and will help me upload more solutions! 

Share with Friends

Leave a Reply