# The derivative of cos and sin. Differentiating sinf(x) and cosf(x).

The derivative of y = cosf(x) is dy/dx = -f’(x)sinf(x).

The derivative of y = sinf(x) is dy/dx = -f’(x)cosf(x).

Just remember that cosx goes to –sinx and sinx goes to cosx. Let’s take a look at some examples of differentiating cos and sin.

Example 1

Find dy/dx if y = cos(4x-2).

First write down f(x) and differentiate this function to give f'(x) (This goes at the front of your answer)

Here f(x) is 4x-2 so f’(x) is 4. Also the derivative of cos is –sin.

Example 2

Find dy/dx if y = sin(3x+5).

Again write down f(x) and differentiate this function to give f’(x) (This goes at the front of your answer)

Here f(x) is 3x+5 so f’(x) is 3. Also the derivative of sin is cos.

Example 3

Find dy/dx if y = cos8x³

Again write down f(x) and differentiate this function to give f’(x) (This goes at the front of your answer)

Here f(x) is 8x³ so f’(x) is 24x². Also the derivative of cos is –sin.

Example 4

Find dy/dx if y = sin(9x⁴).

Again write down f(x) and differentiate this function to give f’(x) (This goes at the front of your answer)

Here f(x) is 9x⁴ so f’(x) is 36x³. Also the derivative of sin is cos.