Answered: "Find the derivatives of the function defined as..."

Danelle Albright

Answered question

2021-12-06

Find the derivatives of the function defined as follow

y = \tan^{2} x

Lakisha Archer

Beginner2021-12-07Added 39 answers

Step 1
Given function is

y = \tan^{2} x

.
To find the derivative of the function.
Solution:
Power rule of differentiation states that:

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

Chain rule of differentiation sates that:

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

Step 2
Differentiating the given function with respect to x,

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

= 2 \tan x \cdot \frac{d}{d x} (\tan x)

= 2 \tan x \cdot \sec^{2} x

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

Hence, required derivative is

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

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