Explained: "Find the derivative of f(x)=x2+3x at x. That..." - Plainmath

Travis Fogle

Answered question

2021-11-19

Find the derivative of

f (x) = x^{2} + 3 x

at x. That is, find f′(x).

Answer & Explanation

Harr1957

Beginner2021-11-20Added 18 answers

Step 1
We have to find the derivative of f(x) at x :

f (x) = x^{2} + 3 x

We will use following formula, for derivatives,

\frac{d f (x)}{d x} = f^{'} (x)

\frac{d a x^{n}}{d x} = a n x^{n - 1}

\frac{d x}{d x} = 1

Step 2
So finding derivative with respect to 'x', we get

\frac{d f (x)}{d x} = \frac{d (x^{2} + 3 x)}{d x}

f^{'} (x) = \frac{{d x}^{2}}{d x} + 3 \frac{d x}{d x}

= 2 x^{2 - 1} + 3 \times 1

=2x+3
Hence, value of f'(x) is 2x+3.

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