Calc2.11

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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\,


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