Chain Rule Differentiation

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).

f'(x) = 105(3x + 4)^4.

Chain rule.

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

f'(x) = 7(6x^2-5x)^6(12x-5).

f'(x) = 12x(x^2 + 1)^5.

The Power Rule states that if f(x) = x^n, then f'(x) = n*x^(n-1).

The Product Rule states that if you have two functions u(x) and v(x), then the derivative of their product is u'v + uv'.

The Quotient Rule states that if you have a function that is the quotient of two functions u(x) and v(x), then the derivative is (u'v - uv')/v^2.

Use the formula: f'(x) = n(g(x))^(n-1) * g'(x).