Differentiation of algebraic functions

For an algebraic function f(x) = xⁿ = y

Then dy/dx = nx^n-1

Note that to different a power of a variable, first you multiply the variable by the power, and subtract 1 from the power.

E.g. to differentiate y = x², you bring 2 down and subtract 1 from the power. Which is 2x¹ = 2x.

To differentiate 4x³, we have 4(3)x² = 12x².

Simple right?

Now take these examples.

Examples

Differentiate the following:

Solution

Question: What happened to the 10 above?

Answer: Differentiate a constant, you will get zero.

Exercises

Differentiate the following

Solution

Solution

Watch a complete lecture on differentiation of polynomial functions.

• Differentiation of exponential functions