Question

What is s'(x) when s(x) = 5(ek)-4? Select the correct answer below: 0 :'(x) = -1 o ( s'(x) = -20e-3 s'(x) = 5e 4 s'(x) = -20e-4x Let h(x) f(x) where f(x) = 3x2 – 3 and g(x) = ln(x). What is h'(x)? 8(x)

Answer 1

To find s'(x), differentiate s(x) using the chain rule. To find h'(x), differentiate h(x) using the product rule.

Step-by-step explanation:

To find s'(x), we need to differentiate the function s(x) = 5(e^(-4x)).

Using the chain rule, we can differentiate the function as follows:

s'(x) = 5 * (-4)e^(-4x) = -20e^(-4x).

So, the correct answer is s'(x) = -20e^(-4x).

To find h'(x), we need to differentiate the function h(x) = f(x) * g(x), where f(x) = 3x^2 - 3 and g(x) = ln(x).

Using the product rule, we can differentiate the function as follows:

h'(x) = f'(x) * g(x) + f(x) * g'(x).

Calculating the derivatives, we have f'(x) = 6x and g'(x) = 1/x.

Substituting the values into the equation, we get:

h'(x) = (6x * ln(x)) + ((3x^2 - 3) * (1/x)).

Therefore, the expression h'(x) = 6x * ln(x) + (3x - 3)/x represents the derivative of h(x).