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Clifland

Answered question

2021-09-17

Find the derivative of the function using shortcut rules.

y = 4 x^{2} + 13 x + 13

Answer & Explanation

Alannej

Skilled2021-09-18Added 104 answers

Step 1
Consider the function

y = 4 x^{2} + 13 x + 13

To find the derivative of the function, use below rules of derivative
Power rule of derivative

\frac{d}{d x} (x^{n}) = n x^{n - 1}

and the derivative of a constant is zero.
Step 2
So, on differentiating the given function with respect to x using the power rule of derivatives, we get

\frac{d}{d x} (y) = \frac{d}{d x} (4 x^{2} + 13 x + 13)

\Rightarrow \frac{d y}{d x} = \frac{d}{d x} (4 x^{2}) + \frac{d}{d x} (13 x) + \frac{d}{d x} (13)

\Rightarrow \frac{d y}{d x} = 4 \cdot \frac{d}{d x} (x^{2}) + 13 \cdot \frac{d}{d x} (x) + 0

\Rightarrow \frac{d y}{d x} = 4 \cdot (2 x^{2 - 1}) + 13 \cdot (1)

\Rightarrow \frac{d y}{d x} = 4 \cdot (2 x^{1}) + 13

\Rightarrow \frac{d y}{d x} = 8 x + 13

Thus, the derivative of the given function is

\frac{d y}{d x} = 8 x + 13

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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