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Edexcel A-level Maths Differentiation of trigonometric functions

Differentiation of trigonometric functions

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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 = βˆ’sinx and d(tanx)/dx = secΒ²x.

Differentiating trigonometric functions

Equations involving trigonometric reciprocals can be differentiated using the basic rules of differentiation by using the following results: d(cotx)/dx = βˆ’cosecΒ²x, d(secx)/dx = secxtanx and d(cosecx)/dx = βˆ’cosecxcotx.

Differentiating trigonometric reciprocals

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

Differentiating trigonometric functions with the chain rule

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

Differentiating trigonometric functions without the chain rule

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What is the derivative of f(x) = cosx + sinΒ²x?

Edexcel A-level Maths Differentiation of trigonometric functions What is the derivative of f(x) = cosx + sinΒ²x?
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2

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Find the derivative of y = 8tanΒ³x.

Edexcel A-level Maths Differentiation of trigonometric functions Find the derivative of y = 8tanΒ³x.
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3

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

Edexcel A-level Maths Differentiation of trigonometric functions Differentiate the following function: f(x) = 1/tanx + secx.
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4

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Prove that the derivative of cotx is βˆ’cosecΒ²x.

Edexcel A-level Maths Differentiation of trigonometric functions Prove that the derivative of cotx is βˆ’cosecΒ²x.
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5

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Find the derivative of f(x) = (10 + secx)/(7 + xΒ²).

Edexcel A-level Maths Differentiation of trigonometric functions Find the derivative of f(x) = (10 + secx)/(7 + xΒ²).
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6

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Use the Chain rule to find the derivative of y = (tanx + secx)⁡.

Edexcel A-level Maths Differentiation of trigonometric functions Use the Chain rule to find the derivative of y = (tanx + secx)⁡.
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7

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Use the Chain rule to evaluate the derivative of y = cosec(15 βˆ’ x⁴) at x = 1 in radians.

Edexcel A-level Maths Differentiation of trigonometric functions Use the Chain rule to evaluate the derivative of y = cosec(15 βˆ’ x⁴) at x = 1 in radians.
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8

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What is the derivative of the equation of the given graph?

Edexcel A-level Maths Differentiation of trigonometric functions What is the derivative of the equation of the given graph?
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9

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What is the derivative of y = x⁡ + tanx + cotx?

Edexcel A-level Maths Differentiation of trigonometric functions What is the derivative of y = x⁡ + tanx + cotx?
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10

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Find the derivative of y = (8x + xΒ²)/cosx.

Edexcel A-level Maths Differentiation of trigonometric functions Find the derivative of y = (8x + xΒ²)/cosx.
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