Derivatives of trig and chain rule with trig

Front

What is the derivative of f(x) = tan(x)?

Back

f'(x) = sec^2(x)

Front

What is the derivative of f(x) = cos(x)?

Back

f'(x) = -sin(x)

Front

What is the derivative of f(x) = sin(x)?

Back

f'(x) = cos(x)

Front

What is the derivative of f(x) = sec(x)?

Back

f'(x) = sec(x)tan(x)

Front

What is the derivative of f(x) = csc(x)?

Back

f'(x) = -csc(x)cot(x)

Front

What is the derivative of f(x) = cot(x)?

Back

f'(x) = -csc^2(x)

Front

What is the chain rule in calculus?

Back

The chain rule states that if a function y = f(g(x)), then the derivative dy/dx = f'(g(x)) * g'(x).

Front

Find dy/dx if y = (sin(x))^5.

Back

dy/dx = 5(sin(x))^4 * cos(x)

Front

Find dy/dx if y = (cos(x))^3.

Back

dy/dx = -3(cos(x))^2 * sin(x)

Front

Find dy/dx if y = (csc(x) + 1)^7.

Back

dy/dx = -7(csc(x) + 1)^6 * csc(x)cot(x)