How do you use the product rule to find the derivative of y=sqrt(x)*cos(x) ?
1 Answer
The product rule states:
d/dx[f(x) * g(x)] = f'(x)*g(x) + f(x)*g'(x)
So, if we are trying to find the derivative of
Then, by the product rule, we have:
d/dx[sqrt(x) * cosx] = d/dx[sqrt(x)]*cosx + sqrt(x)*d/dx[cosx]
So, now we will substitute into our little formula:
d/dx[sqrt(x) ⋅ cosx] = 1/2 x^(-1/2)⋅cosx + sqrt(x)⋅(-sin x)
Recalling that
d/dx[sqrt(x) ⋅ cosx] = cosx/(2sqrt(x)) - sinx sqrt(x)
And there is our derivative. Remember, when you're differentiating radicals, it's always helpful to rewrite things with rational exponents. That way, you can find derivatives easily using the power rule.