Calc2.11

From Exampleproblems

Find the derivative of $f(x)\,$ with respect to $x\,$ : $f(x)=8x^5+4x^4+6x^3+x+7\,$

For this problem, just use the power rule on every term seperately because the derivative of a sum is equal to the sum of the derivatives of the parts.

$f'(x)=8(5)x^{5-1}+4(4)x^{4-1}+6(3)x^{3-1}+x^{1-1}\,$

Remember anything to the $0\,$ power other than $0\,$ is just $1\,$ so $x^{1-1}=x^0=1\,$ . Simplify the exponents and constants and we get

$f'(x)=40x^4+16x^3+18x^2+1\,$