Derivatives - Chain, Implicit, Inverse Trig

Front

What is the Chain Rule in calculus?

Back

The Chain Rule is a formula for computing the derivative of the composition of two or more functions. If y = f(g(x)), then the derivative is given by dy/dx = f'(g(x)) * g'(x).

Front

Define Implicit Differentiation.

Back

Implicit Differentiation is a technique used to find the derivative of a function defined implicitly by an equation involving both x and y, rather than explicitly solving for y.

Front

What is the derivative of y = log_a(x)?

Back

The derivative of y = log_a(x) is given by dy/dx = 1/(x * ln(a)).

Front

How do you differentiate y = a^(u(x)) where a is a constant?

Back

The derivative is given by dy/dx = a^(u(x)) * ln(a) * u'(x).

Front

What is the formula for the derivative of a product of two functions?

Back

The Product Rule states that if u(x) and v(x) are functions, then the derivative of their product is given by (uv)' = u'v + uv'.

Front

What is the formula for the derivative of a quotient of two functions?

Back

The Quotient Rule states that if u(x) and v(x) are functions, then the derivative of their quotient is given by (u/v)' = (u'v - uv')/v^2.

Front

Find the derivative of f(x) = x^n where n is a constant.

Back

The derivative is f'(x) = n*x^(n-1).

Front

What is the derivative of sin(x)?

Back

The derivative of sin(x) is cos(x).

Front

What is the derivative of cos(x)?

Back

The derivative of cos(x) is -sin(x).

Front

What is the derivative of e^x?

Back

The derivative of e^x is e^x.