Differentiation

For a real variable $t$ , use the quotient rule and the known derivatives of $\sin t\,$ and $\cos t\,$ to demonstrate that:

a.

\frac{d}{dt}(\tan t) = \sec^2 t

[3]

b.

\frac{d}{dt}(\sec t) = \sec t \tan t

[3]

c.

\frac{d}{dt}(\cot t) = -\csc^2 t

[3]

d.

\frac{d}{dt}(\csc t) = -\csc t \cot t

[3]

For a real variable $t$ , use the quotient rule and the known derivatives of $\sin t\,$ and $\cos t\,$ to demonstrate that:

a.

\frac{d}{dt}(\tan t) = \sec^2 t

[3]

b.

\frac{d}{dt}(\sec t) = \sec t \tan t

[3]

c.

\frac{d}{dt}(\cot t) = -\csc^2 t

[3]

d.

\frac{d}{dt}(\csc t) = -\csc t \cot t

[3]

Differentiation Questions