Differentiation

DifferentiationBy Sanjna

Differentiation

1-The derivative of f is denoted by f (x) or if y = f (x) then derivative is dy/dx or y

2-The process of findingderivative of a function is called differentiation. We also use the phrase differentiate f (x) with respect to x to mean find f (x).

FormulaeBasic set of derivatives

-Derivative of constants like 1,2 .... is always 0.- d(ax)/dx = a where a is a constant.

Result :d(u+v)/dx= du/dx + dv/dxd(u-v)/dx = du/dx - dv/dx

Example 1

Differentiate function with respect to x:f(x)=x^2

When f(x) = x^n then f(x)=nx^(n-1)Here n= 2

f(x)= 2.x^(2-1)=2xf(x)=2x

Example 2

Differentiate function with respect to x:

f(x)=2x+4

Here we will use the addition result of derivatives.

f(x)= d(2x+4 )/x=d(2x)/dx + d(4)/dx = 2 + 0 ............[ check formula slide for ax and constant.]f(x)=2

Assessment

Differentiate function with respect to x:

f(x)=3x^2+7

Thanks

Sanjna

Phone:7498524452Email:sanjnad7@gmail.comSkype:sanjna.balaji