Differentiation of trigonometric function

Differentiation deals with rates of change. That is how one quantity varies with respect to another quantity. The rate of change of y with respect to x for a straight line is constant. However, this is different for a curve. Differentiating a function y = f (x) gives a gradient function written as dy/dx or f^-1 (x).

Examples

Trigonometric Derivatives

Multiple Choice

$$\frac{\text{d}}{\text{d}y}\left(\sin x\right)$$  

• $$\cos x$$  

• $$-\cos x$$  

• $$\sin^{-1}x$$  

• $$\frac{1}{\sin x}$$  

• $$\sin x\cos x$$  

Multiple Choice

$$\frac{\text{d}}{\text{d}y}\left(\cos x\right)$$  

• $$-\sin x$$  

• $$\sin x$$  

• $$\cos^{-1}x$$  

• $$\frac{1}{\cos x}$$  

• $$-\sin x\cos x$$  

Multiple Choice

$$\frac{\text{d}}{\text{d}y}\left(\tan x\right)$$  

• $$\sec^2x$$  

• $$-\sec^2x$$  

• $$\tan^{-1}x$$  

• $$\frac{1}{\tan x}$$  

• $$\sec x$$  

Multiple Choice

$$\frac{\text{d}}{\text{d}y}\left(\sec x\right)$$  

• $$\sec x\tan x$$  

• $$-\sec x\tan x$$  

• $$\sec^{-1}x$$  

• $$\frac{1}{\sec x}$$  

• $$\csc x\cot x$$  

Multiple Choice

$$\frac{\text{d}}{\text{d}y}\left(2\sin x+x^3\right)$$  

• $$2\cos x+3x^2$$  

• $$-2\cos x+3x^2$$  

• $$2\cos x+4x^4$$  

• $$2\cos x+2x^2$$  

• $$-2\cos x+2x^2$$  

Multiple Choice

$$\frac{\text{d}}{\text{d}y}\left(-3\cos x-4x^2\right)$$  

• $$3\sin x-8x$$  

• $$-3\sin x-8x$$  

• $$3\sin x-4x$$  

• $$3\sin x-12x^3$$  

• $$-3\sin x-4x$$  

Multiple Choice

 Find  $$\frac{\text{d}y}{\text{d}x}$$   of y = ln (6x+1)

• $$\frac{1}{6x+1}$$  

• $$\frac{6}{6x+1}$$  

• $$\frac{1}{6x}$$  

• 6

Multiple Choice

 Find dy/dx for  $$y=e^{6x}$$  

• $$e^{6x}$$  

• $$6e^{6x}$$  

• $$e^{6x-1}$$  

• $$6xe^{6x-1}$$  

Multiple Choice

Find dy/dx for y= cos 4x

• dy/dx = -4 sin 4x

• dy/dx=sin 4x

• dy/dx = - 4 cos 4x

• dy/dx = 4 sin 4x

Multiple Choice

find the expression for the derivative of the following expression: $$-5\ \cos\ x$$  

• $$5\ \sin\ x$$  

• $$-5\ \sin\ x$$  

• $$5\ \cos\ x$$  

• $$-5\ \cos\ x$$  

Multiple Choice

find the expression for the derivative of the following expression: $$2\ \sin\ \left(4-3x\right)$$  

• $$-6\ \cos\ \left(4-3x\right)$$  

• $$6\ \cos\ \left(4-3x\right)$$  

• $$2\ \cos\ \left(4-3x\right)$$  

• $$-2\ \cos\ \left(4-3x\right)$$  

Multiple Choice

$$If\ y\ =\ e^{\sec x}\ then\ \frac{\text{d}y}{\text{d}x}=$$  

• $$\sec x\tan x.e^{\sec x}$$

• $$e^{\sec x}$$  

• $$e^{\sec x.\tan x}$$  

• $$\sec x.e^{\sec x-1}$$