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

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Answer 1 · 2018-03-02T12:12:09

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

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The derivative of the given function is represented as:

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

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

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

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#=\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)#

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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}#

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So that by applying these rules, we get:

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

Simplify to get:

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

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That's it!