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This mock test of Test: Sum And Difference Rule for JEE helps you for every JEE entrance exam.
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QUESTION: 1

The derivation of 40√x - 20

Solution:

dy/dx = 40x^{½} - 20

dy/dx = 40x^{½}-1 * 20 - 0

= 40/2(x)^{½}

20/(x)1/2

QUESTION: 2

Solution:

Since the number of terms is finite, just differentiate term by term using the power rule.

dy/dx = 0 + 1 + 2x/2! + 3x2/3! + ... + nx^{n-1}/n!

dy/dx = 1 + x + x2/2! + ... + xn-1/(n -1)!

Compare dy/dx to y and note that the last term of y, which is xn/n!, is not in dy/dx, while all the other terms of y are in dy/dx.

Then dy/dx = y - x^{n}/n!

⇒ dy/dx + x^{n}/n! = y

QUESTION: 3

Solution:

y = cosecx

= 1/sinx= (sinx)^{−1}

⇒ dy/dx=−(sinx)^{−2} × d/dx(sinx)

= −cosx/sin^{2x}

= −cosx/sinx ×(1/sinx)

= −cot x cosec x

QUESTION: 4

Solution:

QUESTION: 5

Find the dervative of 5 sin x - 11

Solution:

y = 5 sin x - 11 cosx + 1/x^{2}

dy/dx = 5 cosx - 11(-sinx) + (-2/x^{3})

= 5cosx + 11sinx - 2/x^{3}

QUESTION: 6

The dervative of the function 3x^{2} - x is :

Solution:

dy/dx = 3x^{2}-x

dy/dx = 3(2)x^{(2-1) }- 1x^{(1-1)}

= 6x-1

QUESTION: 7

The derivate of the function sin x + cos x is :

Solution:

Y=sinx+cosx

dy/dx=cosx-sinx

QUESTION: 8

The function, f(x) = and f(a) = 0, is

Solution:

QUESTION: 9

The derivative of the function f(x) = 2x^{2}+3x-3 at x = – 2 is:

Solution:

2x^{2 }+ 3x - 3 =0

dy/dx = 4x + 3

At x = -2

4(-2) + 3 = -5

QUESTION: 10

The derivate of x^{3} - 20x at x = 10 is :

Solution:

Y=x^{3}-20x

dy/dx=3x^{2}-20

(dy/dx) at x=10 is

=3×100-20

=280

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