3. Techniques of Differentiation

Finding Derivative Values

In Exercises 67–72, find the value of (f ∘ g)' at the given value of x.

f(u) = u + 1/cos²u, u = g(x) = πx, x = 1/4

Finding Derivative Values

In Exercises 67–72, find the value of (f ∘ g)' at the given value of x.

f(u) = cot(πu/10), u = g(x) = 5√x, x = 1

In Exercises 41–58, find dy/dt.

y = √(3t + (√2 + √(1 − t)))

In Exercises 41–58, find dy/dt.

y = tan²(sin³(t))

In Exercises 41–58, find dy/dt.

y = 4 sin(√(1 + √t))

In Exercises 41–58, find dy/dt.

y = (1/6)(1 + cos²(7t))³

In Exercises 41–58, find dy/dt.

y = (1 + tan⁴(t/12))³

In Exercises 41–58, find dy/dt.

y = ((3t − 4) / (5t + 2))⁻⁵

In Exercises 41–58, find dy/dt.

y = (t⁻³/⁴ sin(t))⁴/³

In Exercises 41–58, find dy/dt.

y = (t tan(t))¹⁰

In Exercises 41–58, find dy/dt.

y = (1 + cos(2t))⁻⁴

In Exercises 41–58, find dy/dt.

y = sin²(πt − 2)

Find the derivatives of the functions in Exercises 19–40.

q = sin(t / (√t + 1))

Find the derivatives of the functions in Exercises 19–40.

g(t) = (1 + sin(3t) / (3 − 2t))⁻¹

Find the derivatives of the functions in Exercises 19–40.

f(x) = √(7 + x sec x)