Differentiation

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Question 68

A calculus student is verifying the derivative formulas for trigonometric functions of $u$ . Using the derivatives $ddu(sin⁡u)=cos⁡u\displaystyle \frac{d}{du}(\sin u) = \cos u$ and $ddu(cos⁡u)=−sin⁡u\displaystyle \frac{d}{du}(\cos u) = -\sin u$ , help them prove that:

a.

\frac{d}{du}(\tan u) = \sec^2 u

[3]

b.

\frac{d}{du}(\sec u) = \sec u \tan u

[3]

c.

\frac{d}{du}(\cot u) = -\csc^2 u

[3]

d.

\frac{d}{du}(\csc u) = -\csc u \cot u

[3]

Differentiation

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Question 68

A calculus student is verifying the derivative formulas for trigonometric functions of $u$ . Using the derivatives $ddu(sin⁡u)=cos⁡u\displaystyle \frac{d}{du}(\sin u) = \cos u$ and $ddu(cos⁡u)=−sin⁡u\displaystyle \frac{d}{du}(\cos u) = -\sin u$ , help them prove that:

a.

\frac{d}{du}(\tan u) = \sec^2 u

[3]

b.

\frac{d}{du}(\sec u) = \sec u \tan u

[3]

c.

\frac{d}{du}(\cot u) = -\csc^2 u

[3]

d.

\frac{d}{du}(\csc u) = -\csc u \cot u

[3]

Differentiation

Question 68

Differentiation Questions

Differentiation

Question 68

Differentiation Questions