The table above gives the values of the differentiable functions f and g and their derivatives at x=4. What is the value of ⅆ/ⅆx(f(x)g(x)) at x=4 ?
To find the value of ⅆ/ⅆx(f(x)g(x)) at x=4, we can use the product rule of differentiation
To find the value of ⅆ/ⅆx(f(x)g(x)) at x=4, we can use the product rule of differentiation. The product rule states that if we have two differentiable functions f(x) and g(x), then the derivative of their product is given by:
ⅆ/ⅆx(f(x)g(x)) = f'(x)g(x) + f(x)g'(x)
Now let’s apply this rule using the values given in the table:
f(4) = 5
f'(4) = 2
g(4) = 3
g'(4) = 4
Plugging these values into the product rule formula, we get:
ⅆ/ⅆx(f(x)g(x)) = f'(x)g(x) + f(x)g'(x)
ⅆ/ⅆx(f(x)g(x)) = f'(4)g(4) + f(4)g'(4)
ⅆ/ⅆx(f(x)g(x)) = 2 * 3 + 5 * 4
ⅆ/ⅆx(f(x)g(x)) = 6 + 20
ⅆ/ⅆx(f(x)g(x)) = 26
Therefore, the value of ⅆ/ⅆx(f(x)g(x)) at x=4 is 26.
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