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

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What is the derivative of f(x) = cosx + sin²x?

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2

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Find the derivative of y = 8tan³x.

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3

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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 −cosec²x.

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5

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Find the derivative of f(x) = (10 + secx)/(7 + x²).

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6

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Use the Chain rule to find the derivative of y = (tanx + secx)⁵.

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7

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Use the Chain rule to evaluate the derivative of y = cosec(15 − 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?

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9

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What is the derivative of y = x⁵ + tanx + cotx?

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10

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Find the derivative of y = (8x + x²)/cosx.

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