Question

differentiate tan8x

Answer 1

Answer:

• 8.sec²(8x)

Steps:

This is a question of differentiating with the usage of Chain Rule.

According to Chain Rule Differentiation,

$\boxed{\dfrac{dy}{dx} = \dfrac{dy}{dt} \times \dfrac{dt}{dx}}$

This is usually done if there is more than 1 function to be differentiated.

In the above question, there are 2 functions.

f(x) = tan (8x) & g(x) = 8x

The given function h(x) is of the form f(g(x))

Hence we first differentiate f(x) with respect to x and later on differentiate g(x) with respect to x. Finally we multiply both to get the differentiation of h(x).

Differentiating f(x) we get:

$\implies \dfrac{d}{dx} (f(x)) = \dfrac{d}{dx}(tan\:8x)\\\\\\\implies \dfrac{d}{dx}(f(x)) = sec^2(8x) \hspace{20} ...(i)$

Differentiating g(x) we get:

$\implies \dfrac{d}{dx}(g(x)) = \dfrac{d}{dx}(8x)\\\\\\\implies \dfrac{d}{dx}(g(x)) = 8 \hspace{20} ...(ii)$

Multiplying (i) and (ii) we get:

$\implies \dfrac{d}{dx}(h(x)) = \dfrac{d}{dx} (tan(8x) ) = sec^2(8x) \times 8\\\\\\\implies \boxed{ \dfrac{d}{dx}(tan(8x) = 8.sec^2(8x)}$

Hence the derivative of Tan (8x) is 8.sec²(8x)

Answer 2

Answer:

Use Chain Rule on tan 8x. Let u =

8x. Use Trigonometric Differentiation: the derivative of tan u is sec? u.

d sec (8æ)(8x)

dx

d 2 Use Power Rule: 4 x" = nx"-1. da

8 sec (8.2)

Done