FIND THE DERIVATIVE OF THE FUNCTION
f (x) = 10e^x
The derivative of e^x is e^x. To determine the derivative apply the constant multiple rule
To find the derivative of the function f(x) = 10e^x, we will use the chain rule.
The chain rule states that if we have a function in the form g(h(x)), then the derivative of g(h(x)) is g'(h(x)) times h'(x).
In our case, g(u) = 10e^u and h(x) = x.
First, let's find the derivative of g(u) with respect to u.
The derivative of e^u with respect to u is simply e^u.
So g'(u) = 10e^u.
Next, let's find the derivative of h(x) with respect to x.
The derivative of x with respect to x is simply 1.
So h'(x) = 1.
Now, we can use the chain rule to find the derivative of f(x).
f'(x) = g'(h(x)) times h'(x)
Substituting the values we found earlier:
f'(x) = (10e^x) times 1
Simplifying:
f'(x) = 10e^x
Therefore, the derivative of the function f(x) = 10e^x is f'(x) = 10e^x.
To find the derivative of the function f(x) = 10e^x, we can use the chain rule.
The chain rule states that if we have a composition of functions, the derivative of the composition is the derivative of the outer function multiplied by the derivative of the inner function.
In this case, the outer function is f(x) = 10e^x, and the inner function is g(x) = e^x.
First, let's find the derivative of the inner function: g'(x) = d/dx(e^x).
The derivative of e^x is simply e^x itself. So g'(x) = e^x.
Now, let's find the derivative of the outer function: f'(x) = d/dx(10e^x).
Using the chain rule, we can write f'(x) = g'(x) * (derivative of the outer function).
Substituting g'(x) = e^x, we have f'(x) = e^x * (derivative of the outer function).
The derivative of the outer function, d/dx(10e^x), is simply 10e^x, as the derivative of e^x is e^x and the constant 10 remains unchanged.
So, f'(x) = 10e^x * e^x = 10e^2x.
Therefore, the derivative of the function f(x) = 10e^x is f'(x) = 10e^2x.