Find the derivative of the function f(x) = 4x + 5 x 3x + 7 x - Vidyadip

Question

Find the derivative of the function $f(x) = \frac{{4x + 5\sin x}}{{3x + 7\cos x}}$

✓

Answer

Here $f(x) = \frac{{4x + 5\sin x}}{{3x + 7\cos x}}$
$\therefore\;f'(x)=\frac{(3x+7\cos x)\frac d{dx}(4x+5\sin x)-(4x+5\sin x)\frac d{dx}(3x+7\cos x)}{{(3x+7\cos x)}^2}$
$ = \frac{{(3x + 7\cos x)(4+ 5\cos x) - (4x + 5\sin x)(3 - 7\sin x)}}{{{{(3x + 7\cos x)}^2}}}$
$=\;\frac{12x+15x\cos x+28\cos x+35\cos^2x-12x+28x\sin x-15\sin x+35\;\sin^2x}{{(3x+7\cos x)}^2}$
$ = \frac{{15x\cos x + 28\cos x + 28x\sin x - 15\sin x + 35({{\cos }^2}x + {{\sin }^2}x)}}{{{{(3x + 7\cos x)}^2}}}$
$ = \frac{{15x\cos x + 28\cos x + 28x\sin x - 15\sin x + 35}}{{{{(3x + 7\cos x)}^2}}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 2 marks)" from LIMITS AND DERIVATIVES→LIMITS AND DERIVATIVES — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let N be the set of natural numbers. Define a real valued function f : $N \rightarrow N$ by f (x) = 2x + 1. Using this definition, complete the table given below

x	1	2	3	4	5	6	7
y	f (1) = ...	f (2) = ...	f (3) = ...	f (4) = ...	f (5) = ...	f (6) = ...	f (7) = ...

The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.

Solve $\sqrt 2 \;{x^2} + x + \sqrt 2 = 0$

Solve the inequality: $6 \leq- 3(2x - 4) < 12$

Solve the following linear inequations in R: x + 5 > 4x - 10

Find x in the following. $\frac{1}{6!}+\frac{1}{7!}=\frac{\text{x}}{8!}$

Differentiate the following functions with respect to x:$\frac{1}{\text{ax}^2+\text{bx}+\text{c}}$

Prove that $\begin{equation} \frac{\cos 7 x+\cos 5 x}{\sin 7 x-\sin 5 x}=\cot x \end{equation}$

Find the domain and range of the real function f defined by $f(x) = \sqrt {x - 1} $

There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answers are there to this question?