Trignometric Derivatives Learning

The word trigonometry derived from the words trigonon and metron. The meaning of “trigonon” is triangle and “metron” meaning measurement. Thus, the word exactly means the science, which deals with the measurement of triangles .The derivative of a constant is zero. There is no exact value for the integral. Integration is one of most important study of calculus in mathematics. We require to find f(x) where, d/dx f(x) = g(x) and g(x) is given.

Differential calculus formula for trigonometric term:

1.   `d / dx` (x n ) = n xn-1

2.   ` d/dx` (cosec x) = −cosec x.cot x

3.   `d/dx` (sin x) = cos x

4.   `d/dx` (sec x) = sec x.tan x

5.   `d/dx` (cos x) = −sin x

6.   ` d/dx` (cot x) = −cosec2 x

7.   ` d/dx` (tan x) = sec2x

Trigonometric derivative learning problems:

Trigonometric derivatives learning problem 1: Differentiate sin 3x cos 5x with respect to x:

Solution:

Let   y  = sin 3x cos 5x

= (1/2) [2 cos 5x sin 3x]

= (1/2)[sin (5x + 3x) - sin (5x - 3x)]

= (1/2)[sin 8x - sin 2x]

= (1/2) sin 8x - (1/2) sin 2x

` dy/dx`  = (1/2) d/dx (sin 8x) - (1/2) d/dx (sin 2x)

= (1/2)8 cos 8x - (1/2)2 cos 2x

= 4 cos 8x - cos 2x

Answer:

`d/dx ` (sin 3x cos 5x) = 4 cos 8x - cos 2x

My forthcoming post is on Inverse Functions Calculus and neet application will give you more understanding about Algebra.

Trigonometric derivatives learning problem 2: Differentiate sin (cos x2) with respect to x:

Solution:

Let      y = sin (cos x2)

Putting x2 = t and cos x2 = cos t = u,

y = sin u,   u = cos t   and    t = x2

dy/du = cos u, du/dt = -sin t    and dt/dx = 2x

`dy / dx` = [( dy/du) × (du/dt) × (dt/dx)]

= [cos u × (-sin t) × 2x]

= -2x sin t cos u                                                (u = cos t)

= - 2x sin t cos (cos t)                                        (t = x2)

`dy/dx` = -2x sin x2 cos (cos x2).

Answer:

` dy/dx`  = - 2x sin x2 cos (cos x2)

Trigonometric derivatives learning practice problem:

Trigonometric derivatives learning practice problem 1: Differentiate cos2x2 with respect to x:

Answer: `d/dx` (cos2x2 ) = - 4x cos x2sin x2

Is this topic algebra questions hard for you? Watch out for my coming posts.

Trigonometric derivatives learning practice problem 2: Differentiate tan 3x with respect to x:

Answer:` d/dx` (tan 3x) = 3sec23x

Trigonometric derivatives learning practice problem 3: Differentiate cos 4x cos2x with respect to x:

Answer:` d/dx` (cos 4x cos 2x) = - 3 sin 6x - sin 2x