# StudySquare

# OCR A-level Maths Differentiation of trigonometric functions

This page covers the following topics:

1. Differentiating trigonometric functions

2. Differentiating trigonometric reciprocals

3. Differentiating trigonometric functions with the chain rule

4. Differentiating trigonometric functions without the chain rule

Equations involving trigonometric functions can be differentiated using the basic rules of differentiation by using the following results: d(sinx)/dx = cosx, d(cosx)/dx = −sinx and d(tanx)/dx = sec²x.

Equations involving trigonometric reciprocals can be differentiated using the basic rules of differentiation by using the following results: d(cotx)/dx = −cosec²x, d(secx)/dx = secxtanx and d(cosecx)/dx = −cosecxcotx.

The Chain rule can be applied to differentiate equations involving trigonometric functions using the results of their derivatives.

All differentiation rules can be used with the results for the derivatives of trigonometric functions to differentiate equations involving trigonometric functions.

# 1

Find a function for the slope for the given graph.

# 2

Differentiate the following function: g(x) = sec²xcosx/tanx.

# 3

Prove that the derivative of cotx is −cosec²x.

# 4

Differentiate the following function: f(x) = 1/tanx + secx.

# 5

Find the derivative of y = 8tan³x.

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