It is used to measure the sensitivity of one variable (dependent variable) with respect to another variable (independent variable).
Derivatives can be classified into various types based on their order such as first and second-order derivatives.
Consider y = sin2 x
Using the chain rule, differentiate both sides with respect to x
dy/dx = d/dx sin2 x
dy/dx = 2 sin x X d/dx sin x [As d/dx xⁿ = nxⁿ⁻1]
dy/dx = 2 sin x X cos x [As d/dx sin x = cos x]
dy/dx = 2 sin x cos x
dy/dx = sin 2x [As 2 sin x cos x = sin 2 x]
Therefore, the derivative of sin2 x is sin 2x.
What is the derivative of sin2 x?
The derivative of sin2 x is sin 2x.