Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Examples

Example 1 (i)

Example 1 (ii)

Example 1 (iii)

Example 2 (i)

Example 2 (ii) Important

Example 2 (iii) Important

Example 2 (iv)

Example 2 (v)

Example 3 (i) Important

Example 3 (ii) Important

Example 4 (i)

Example 4 (ii) Important

Example 5

Example 6

Example 7 Important

Example 8

Example 9

Example 10 Important

Example 11

Example 12

Example 13 Important

Example 14

Example 15 Important

Example 16

Example 17 Important

Example 18

Example 19 (i) Important

Example 19 (ii)

Example 20 (i)

Example 20 (ii) Important

Example 21 (i)

Example 21 (ii) Important

Example 22 (i) You are here

Example 22 (ii) Important

Last updated at May 29, 2023 by Teachoo

Example 22 Find the derivative of (i) (x^5 − cosx)/sinx Let f(x) = (x^5 − cosx)/sinx Let u = x5 – cos x & v = sin x So, f(x) = (𝑢/𝑣) ∴ f’(x) = (𝑢/𝑣)^′ Using quotient rule f’(x) = (𝑢^′ 𝑣 −〖 𝑣〗^′ 𝑢)/𝑣^2 Finding u’ & v’ u = x5 – cos x u’ = 5. x5 – 1 – ( – sin x) = 5x4 + sin x v = sin x v’ = cos x Now, f’(x) = (𝑢^′ 𝑣 −〖 𝑣〗^′ 𝑢)/𝑣^2 Derivative of xn is nxn – 1 & Derivative of cos x = – sin x (Derivative of sin x = cos x) = ((5x4 + sin〖x) sin x −(cos x)(x5 − cos x) 〗)/sin2x = (5x4 sin〖x + sin 2x − cos x . x5 + cos2 x〗)/(sin2 x) = (−x5 cos〖x + 5x4 sinx + 𝐬𝐢𝐧𝟐 𝐱 + 𝐜𝐨𝐬𝟐 𝐱〗)/(sinx )2 = (−x5 cos〖x + 5x4 sinx + 𝟏〗)/(sinx )2 Thus, f’(x) = (−𝐱𝟓 𝐜𝐨𝐬〖𝐱 + 𝟓𝐱𝟒 𝐬𝐢𝐧𝒙 + 𝟏〗)/(𝐬𝐢𝐧𝐱 )𝟐 (Using sin2x + cos2x = 1)