How to Apply the Product Rule of Differentiation?
In order to calculate the derivative of the function of the form h(x) = f(x)g(x), both f(x) and g(x) should be differentiable functions. We can apply the following given steps to calculate the derivation of a differentiable function h(x) = f(x)g(x) using the product rule.
Step 1: not down the values of f(x) and g(x)
Step 2: calculate the values of f’(x) and g'(x)
And apply the product rule formula
Find f'(x) for the following function f(x) using the product rule: f(x) = x·log x.
Here, f(x) = x·log x
u(x) = x
v(x) = log x
⇒u'(x) = 1
⇒v'(x) = 1/x
⇒f'(x) = [v(x)u'(x) + u(x)v'(x)]
⇒f'(x) = [log x•1 + x•(1/x)]
⇒f'(x) = log x + 1
Result: The derivative of x log x using the product rule is log x + 1.
Y=sinx.cosx differentiated by using the product rule
By using the product rule
calculate the value du/dx and dv/dx
put the value du/dx and dv/dx and u,v
Result: The derivative of sinx.cosx using the product rule is cos2x-sin2x