Derivative Calculator

Enter the expression you wish to differentiate below.

Operators: + , - , *, /, ^ . Constants: e , pi . Functions: sqrt , log (natural logarithm) , sin , cos , tan , sec , csc , cot

The derivative with respect to is:

12*x^2 + 6*x + 2

Solve derivatives using this free online calculator.

The deriver function of the calculator makes it possible to compute function derivations online by using the properties of the derivative on the one hand and the derivatives of the usual functions on the other hand. Derivative calculation obtained is returned after being simplified.

Some basic rules of differentiation:

Some rules of differentiation are a snap to remember and use. These include the constant rule, the power rule, the constant multiple rule, the sum rule, and the rule of difference.

The constant rule: This is simple. f(x)=10 is a horizontal line with a slope of zero, and so its derivative is also zero.

So, for any number a, if f(x)=a, then f'(x)=0.

The rule of feeding:

Say f(x)=x^5. To find its derivative, take the power 5 bring it of the x and then reduce the power by1. That gives you f'(x)=5x^4

Derivative of Exponential function f(x)= ex : f'(x)= ex

Derivative of Exponential function f(x)= ax : f'(x)= ax ln a

Derivative of Natural logarithm function f(x)= ln(x) : f'(x)= 1/x

Derivative of Logarithm function f(x)= log b (x) : f'(x)=1/(xln(b))

Derivative of Sine function f(x)= sin x : f'(x)= cos x

Derivative of Cosine function f(x)= cos x : f'(x)= -sin x