Use the theorems on derivatives to find the derivatives of the following function: f(x)=3x^{5}-2x^{4}-5x+7+4x^{-2}

Sinead Mcgee

Sinead Mcgee

Answered question

2021-05-04

Use the theorems on derivatives to find the derivatives of the following function:
f(x)=3x52x45x+7+4x2

Answer & Explanation

svartmaleJ

svartmaleJ

Skilled2021-05-05Added 92 answers

Step 1
There are two operations addition and substraction in the given function which is a polynomial. We use sum/difference rule of differentiation, (f±g)=f±g
Also we know that the derivative of xa is axa1.
Derivative of a constant is always zero.
Step 2
Given
f(x)=3x52x45x+7+4x2
f(x)=ddx(3x5)ddx(2x4)ddx(5x)+ddx(7)+ddx(4x2)
=15x48x35+08x3
Step 3
Therefore the derivative is given as,
f(x)=15x48x38x35

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