How do you find the derivative of # f(x) = 2e^x  3x^4#?
Remember the sum/difference of derivative rule, which is applied when two function are being added/subtracted up.
Pull out the constant from the derivative. The rule is stated as:
Now at this point, we need to recall the power rule for derivative and exponential function rule. They are stated as:
So that by applying these rules, we get:
Simplify to get:
That's it!
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To find the derivative of f(x) = 2e^x  3x^4, you would differentiate each term separately using the rules of differentiation:

Differentiate the term 2e^x: The derivative of e^x is e^x, so the derivative of 2e^x is 2e^x.

Differentiate the term 3x^4: Apply the power rule, which states that the derivative of x^n is nx^(n1). So, the derivative of 3x^4 is 12x^3.
Therefore, the derivative of f(x) = 2e^x  3x^4 is f'(x) = 2e^x  12x^3.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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