3. Techniques of Differentiation

Find all points on the curve y = tan x, −π/2 < x < π/2, where the tangent line is parallel to the line y = 2x. Sketch the curve and tangent lines together, labeling each with its equation.

Find the derivative of the function.

$h\left(t\right)=\sin \left(t\right)\cos \left(t\right)$

Find the derivative of the function.

$f\left(x\right)=\frac{5\cos x}{2x^3}$

Find the derivative of the function.

$y=\frac{\sin \theta }{2+\cos \theta }$

Find the indicated derivative.

$f^{19}\left(x\right)$ of $f\left(x\right)=\cos x$

Find the indicated derivative.

$d^{1002}/d{x}^{1002}\left(\sin x\right)$

Find the indicated derivative.

$d^{52}y/d{x}^{52}$ of $y=\cos x$

Find the derivative of the function.

$r=\csc x-3\sin x+\tan x$

Find the derivative of the function.

$f\left(x\right)=4x^2\sec x-\sqrt{x}$

Find the derivative of the function.

$y=\frac{\cot \theta }{3+\sec \theta }$

Find an equation of the line tangent to the curve y = sin x at x = 0.

Let f(x) = sin x. What is the value of f′(π)?

Find the derivative of the following functions.

y = sin x + cos x

Find the derivative of the following functions.

y = cos x/sin x + 1

23–51. Calculating derivatives Find the derivative of the following functions.

y = a sin x + b cos x/a sin x - b cos x; a and b are nonzero constants