Resolved: "Compute the derivative using derivative rules. y=tan⁡(x2+4x)"

Kyran Hudson

Answered question

2021-09-16

Compute the derivative using derivative rules.

y = \tan (x^{2} + 4 x)

liannemdh

Skilled2021-09-17Added 106 answers

Step 1
We have to compute the derivative of the function:

y = \tan (x^{2} + 4 x)

We know the formula of derivatives,

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

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

\frac{d \tan x}{d x} = \sec^{2} x

\frac{d \tan f (x)}{d x} = \sec^{2} f (x) \times \frac{d f (x)}{d x}

Step 2
Computing derivative of given function with respect to x and applying above formula, we get

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

= \sec^{2} (x^{2} + 4 x) \times (\frac{d (x^{2} + 4 x)}{d x})

= \sec^{2} (x^{2} + 4 x) \times (\frac{{d x}^{2}}{d x} + 4 \frac{d x}{d x})

= \sec^{2} (x^{2} + 4 x) \times (2 x^{2 - 1} + 4 \times 1)

= \sec^{2} (x^{2} + 4 x) \times (2 x + 4)

= \sec^{2} (x^{2} + 4 x) \times 2 (x + 2)

= 2 (x + 2) \sec^{2} (x^{2} + 4 x)

Hence, derivative of given function is

2 (x + 2) \sec^{2} (x^{2} + 4 x)

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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