Answered: "Use the rules for derivatives to find the..."

sodni3

Answered question

2021-05-25

Use the rules for derivatives to find the derivative of each function defined as follows.

y = 2 \tan 5 x

Elberte

Skilled2021-05-26Added 95 answers

Step 1
Consider the provided function,

y = 2 \tan 5 x

Use the rules for derivatives to find the derivative.
Now, we differentiate with respect to x.

\frac{d}{d x} (y) = \frac{d}{d x} (2 \tan 5 x)

First, we take the constant out side the provided function.

\frac{d}{d x} (y) = 2 \frac{d}{d x} (\tan 5 x)

Step 2
Now, apply the chain rule of the derivative

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

And use the common derivative formula,

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

So,

\frac{d}{d x} (y) = 2 \frac{d}{d x} (\tan 5 x)

= 2 (\sec^{2} (5 x) \frac{d}{d x} (5 x))

= 2 (\sec^{2} (5 x) \cdot 5)

= 10 \sec^{2} (5 x)

Hence.

Jeffrey Jordon

Expert2022-03-24Added 2605 answers

Answer is given below (on video)

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