Let f(3) = 0, f '(3) = 6, g(3) = 1, and g '(3) = 1/3. If h(x) = f(x)*g(x), find h '(3).
Use the rule of products:
h'(x)
=d(f(x)*g(x))/dx
=f(x)*g'(x)+f'(x)*g(x)
For h'(3), substitute f(3),g'(3),f'(3) and g(3) above to evaluate.
Post your answer for a check if you wish.
6(h - 3) if h = -5
To find h'(3), we need to use the product rule for differentiation. The product rule states that if h(x) = f(x) * g(x), then h'(x) = f'(x) * g(x) + f(x) * g'(x).
Given that f(3) = 0, f'(3) = 6, g(3) = 1, and g'(3) = 1/3, we can substitute these values into the product rule formula to find h'(3).
h'(3) = f'(3) * g(3) + f(3) * g'(3)
= 6 * 1 + 0 * 1/3
= 6 + 0
= 6
Therefore, h'(3) = 6.
To find h'(3), the derivative of the function h(x) = f(x) * g(x), we can use the product rule.
The product rule states that if we have two differentiable functions, u(x) and v(x), then the derivative of their product is given by:
(d/dx)(u(x) * v(x)) = u'(x) * v(x) + u(x) * v'(x)
In this case, f(x) and g(x) are given functions, and we are looking for h'(3), the derivative of h(x) evaluated at x = 3.
Given:
f(3) = 0
f'(3) = 6
g(3) = 1
g'(3) = 1/3
Using the product rule, we can find h'(x) as follows:
h'(x) = f'(x) * g(x) + f(x) * g'(x)
Now, we substitute the given values at x = 3:
h'(3) = f'(3) * g(3) + f(3) * g'(3)
h'(3) = 6 * 1 + 0 * 1/3
Simplifying:
h'(3) = 6 + 0
Therefore, h'(3) = 6.