Differentiation Class 12 OP Malhotra Exe-8C ISC Maths Solutions Ch-8 Solutions. In this article you would learn about derivatives of trigonometric functions. Step by step solutions of latest textbook has been given as latest syllabus. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.
Differentiation Class 12 OP Malhotra Exe-8C ISC Maths Solutions Ch-8
| Board | ISC |
| Publications | S Chand |
| Subject | Maths |
| Class | 12th |
| Chapter-8 | Differentiation |
| Writer | OP Malhotra |
| Exe-8(C) | derivatives of trigonometric functions |
Exercise- 8C
Differentiation Class 12 OP Malhotra Exe-8C Solution.
Que-1: Sin²(x²)
Sol: Let y = sin²x² = (sin x²)²
∴ dy/dx=d/dx((sin x²)²) =2sin x² d/dx(sin x²) = 2 sin² cosx². 2x
= 2x sin(2x²) [∵ 2 sin θ cos θ = sin² θ]
Que-2: Sin(1+x²/1-x²)
Sol:
Que-3: x²Sin(1/x)
Sol:
Que-4: √aSin²x +bCos²x
Sol:
Que-5: Cos (1 – x²)²
Sol:Let y = cos (1 – x²)²; Diff both sides of eqn (1) w.r.t x ; we have
dy/dx=-Sin(1 – x²)² d/dx(1 – x²)²= -Sin(1 – x²)²2(1 – x²) d/dx(1 – x²)
=-Sin(1 – x²)²2(1 – x²)(-2x)=4x(1 – x²)²Sin(1 – x²)²
Que-6: Sin²x Cos³x
Sol:
Que-7: Cot (Sin√x)
Sol:
Que-8: √Secx-1/Secx+1
Sol:
Que-9: Find dy/dx if y = Sinx + x²/Cot2x
Sol: Diff both sides w.r.t. x ; we have
dy/dx = (sinx + x²) d/dx tan2x + tan2x d/dx (sinx + x²)
= (sinx + x²)sec² 2x.2 + tan2x (cosx + 2x)
= (2sinx + 2x²)sec² 2x + (cosx + 2x) tan2x
Que-10: If y =(Secx – Tanx/Secx + Tanx), show that dy/dx= -2 Secx/(Secx + Tanx)²
Sol:
Que-11: If f(x)= 9Sinx +Sin3x, find f’(π/3)
Sol:Given f(x) = 9 sin x + sin 3x ; Diff both sides w.r.t. x ; we have
f'(x) = 9 cos x + 3 cos 3x
∴f'(π/3)=9Cos(π/3) + 3Cosπ =9/2 + 3(-1) =3/2
Que-12: Differentiate y=Tanx and show that xSin²x dy/dx = x²Tanx + ySin²x
Sol: Given y = x tan x
Diff eqn (1) both sides w.r.t. x ; we have
dy/dx = x sec² x + tan x
⇒ x sin²x dy/dx = x sin²x [ x sec² x + tan x] = x² tan²x + sin²x (x tan x)
⇒ x sin²x dy/dx = x²tan²x + y sin² x [ using eqn (1)]
Que-13: If y=aSinx + bCosx , show that y² + (dy/dx)² = a² + b²
Sol: Given y = a sin x + b cos x
Diff eqn (1) both sides w.r.t. x ; we have
dy/dx = a cos x – b sin x
on squaring and adding eqn. (1) & eqn. (2) ; we have
y² + (dy/dx)² = (a sin x + b cos x)² + (a cos x – b sin x)²
= a²(sin² x + cos² x) + b²(sin² x + cos² x) – a² + b²
Que-14: If y=√1-Sin2x / 1+Sin2x , show that dy/dx + Sec²(π/4 -x) = 0
Sol:
Que-15: If y=2Tanx/2 , prove taht dy/dx=2/1+Cosx
Sol:Given y = 2 tanx/2, Diff both sides w.r.t. x ; we have
dy/dx=2Sec²x/2 1/2 = 1/Cos²x/2 = 1/1+Cos(2×x/2)/2 = 2/1+Cosx
–: End Differentiation Class 12 OP Malhotra Exe-8C ISC Math Ch-8 Solution :–
Return to :- OP Malhotra ISC Class-12 S Chand Publication Maths Solutions
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