# Understanding Differentiation and Gradient Functions

• Differentiation is one key concept in calculus. It describes the rate of change of one quantity with respect to another. It helps to understand how a quantity changes as it varies.

• The derivative of a function is often referred to as the gradient function because it gives the slope or gradient of the tangent to the function at any point.

• The basic rule to differentiate a power of x is known as the Power Rule: if y = x^n, then dy/dx = n.x^n-1. The ‘n’ moves in front of x and the power is reduced by 1.

• When a constant is attached to a function, we can differentiate it normally and then multiply by that constant. If y = 5x^n, then dy/dx = 5n.x^n-1

# Differentiation of Special Functions

• Differentiating a constant: The derivative of a constant is zero because a constant doesn’t change: if y = c where c is a constant, then dy/dx = 0.

• Differentiating a linear function: For a linear function y = mx, the derivative is just the coefficient of x, m: dy/dx = m.

• Differentiating the sum or difference of functions: The derivative of a sum or difference of functions is the sum or difference of their derivatives.