Chain Rule with Trig d/dx (Delehant)

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. It states that if you have a function f(g(x)), then the derivative f'(g(x)) * g'(x).

Front

Differentiate f(x) = cos(5x^4).

Back

f'(x) = -20x^3 sin(5x^4).

Front

Differentiate f(t) = (t^2 + 2t)^5.

Back

f'(t) = 5(t^2 + 2t)^4(2t + 2).

Front

Differentiate f(x) = (x^6 + 4)^5.

Back

f'(x) = 30x^5(x^6 + 4)^4.

Front

What is the derivative notation for a function f(x)?

Back

Common notations include f'(x), y', dy, and dy/dx.

Front

Which notation is not correct for 'derivative'?

Back

dy is not a correct notation for 'derivative'.

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

If f(x) = g(h(x)), what is the derivative f'(x)?

Back

f'(x) = g'(h(x)) * h'(x) (Chain Rule).

Front

Differentiate f(x) = sin(3x^2).

Back

f'(x) = 6x cos(3x^2).

Front

Differentiate f(x) = e^(2x).

Back

f'(x) = 2e^(2x).