How do you find the derivative of f(x) = 2e^x - 3x^4?

1 Answer
Mar 2, 2018

f^{'}(x)\ =\ 2e^x-12x^3

Explanation:


The derivative of the given function is represented as:

d/dx(f(x))\ =\ d/dx(2e^x-3x^4)

Remember the sum/difference of derivative rule, which is applied when two function are being added/subtracted up.

(f\pm g)^'=f^'\pm g^'

=\frac{d}{dx}(2e^x)-\frac{d}{dx}(3x^4)

Pull out the constant from the derivative. The rule is stated as:

(a\cdot f)^'=a\cdot f^'

=2\frac{d}{dx}(e^x)-3\frac{d}{dx}(x^4)

Now at this point, we need to recall the power rule for derivative and exponential function rule. They are stated as:

\frac{d}{dx}(e^x)=e^x" "and" "\frac{d}{dx}(x^a)=a\cdot x^{a-1}

So that by applying these rules, we get:

=2e^x-3\cdot 4x^{4-1}

Simplify to get:

f^{'}(x)\ =\ 2e^x-12x^3

That's it!