Find the derivative of the given function.f(x)=−3ex+5x−2f(x)=-3e^x+5x-2f(x)=−3ex+5x−2

− 3 e x + 5 -3e^x+5 − 3 e x + 5

Find the derivative of the given function. f ( x ) = − 3 e x + 5 x − 2 f(x)=-3e^x+5x-2 f ( x ) = − 3 e x + 5 x − 2

this problem, we're asked to find the derivative of the function f of x equals negative 3 times e to the x plus 5x minus 2. So let's go ahead and get started. Now we wanna find our derivative here, f prime of x. Now since we're adding a bunch of different things together, we can look at each of these derivatives individually and just add and subtract them accordingly. So looking at this first term here, negative 3e to the x, remember, the derivative of e to the x is just e to the x. X. So if I slap a constant on in the front of it, I just need to keep that constant when I take the derivative. So this is still negative 3 e to the x. Then looking at this next term, 5x, the derivative of 5x is just 5. Then, finally, the derivative of a constant is 0, so I don't have to worry about it here. And this is my full derivative. If you have any questions, let us know, and let's keep practicing.

Find the derivative of the given function. f ( x ) = − 3 e x + 5 x − 2 f(x)=-3e^x+5x-2 f ( x ) = − 3 e x + 5 x − 2

− 3 e x + 5 -3e^x+5 − 3 e x + 5

− 3 e x ln ⁡ ⁡ 3 + 5 -3e^{x}\ln⁡3+5 − 3 e x ln ⁡3 + 5

− 3 e x + 5 x − 2 -3e^x+5x-2 − 3 e x + 5 x − 2

4. Derivatives of Exponential & Logarithmic Functions

Derivatives of Exponential & Logarithmic Functions

Business Calculus

4. Derivatives of Exponential & Logarithmic Functions

Derivatives of Exponential & Logarithmic Functions

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Multiple Choice

Find the derivative of the given function.
$f(x)=-3e^x+5x-2$

$e^x+5$

$-3e^x+5$

$-3e^{x}\ln3+5$

$-3e^x+5x-2$

Verified step by step guidance

Step 1: Identify the function to differentiate. The given function is f(x) = -3e^x + 5x - 2. This is a combination of exponential, linear, and constant terms.

Step 2: Recall the derivative rules. For exponential functions, the derivative of e^x is e^x. For linear terms like 5x, the derivative is the coefficient (5). For constants like -2, the derivative is 0.

Step 3: Apply the derivative rules term by term. Differentiate -3e^x to get -3e^x. Differentiate 5x to get 5. Differentiate -2 to get 0.

Step 4: Combine the results. Add the derivatives of each term together: (-3e^x) + (5) + (0).

Step 5: Simplify the expression. The final derivative is f'(x) = -3e^x + 5.

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