Q. 27

# Differentiate in two ways, using product rule and otherwise, the function(1 + 2tan x)(5 + 4 cos x). Verify that the answers are the same.

Let, y = (1 + 2 tan x)(5 + 4 cos x)

y = 5 + 4 cos x + 10 tan x + 8 tan x cos x

y = 5 + 4 cos x + 10 tan x + 8 sin x { tan x cos x = sin x}

Differentiating y w.r.t x – Using algebra of derivatives, we have – Use formula of derivative of above function to get the result.  …equation 1

Derivative using product rule –

We have to find dy/dx

As we can observe that y is a product of two functions say u and v where,

u = (1 + 2tan x) and v = (5 + 4cos x)

y = uv

As we know that to find the derivative of product of two function we apply product rule of differentiation.

By product rule, we have – …equation 2

As, u = (1 + 2tan x)   …..equation 3 { }

As, v = 5 + 4cos x   …equation 4 { }

from equation 2, we can find dy/dx using equation 3 & 4, we get –  sin x = tan x cos x , so we get –   [ 1 – sin2 x = cos2 x ] Hence, ….equation 5

Clearly from equation 1 and 5 we observed that both equations gave identical results.

Hence, Results are verified

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 