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. 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

6. Derivatives of Inverse, Exponential, & Logarithmic Functions

Derivatives of Exponential & Logarithmic Functions

Calculus

6. Derivatives of Inverse, 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

Identify the function for which you need to find the derivative. The function given is $ f(x) = -3e^x + 5x - 2 $.

Apply the derivative rules: The derivative of $ e^x $ is $ e^x $, and the derivative of $ x $ is 1. Constants like -2 have a derivative of 0.

Differentiate each term separately: For $ -3e^x $, use the constant multiple rule to get $ -3e^x $. For $ 5x $, the derivative is 5. The derivative of the constant -2 is 0.

Combine the derivatives of each term to form the derivative of the entire function: $ f'(x) = -3e^x + 5 $.

Verify your result by checking each step and ensuring that the rules of differentiation have been applied correctly.

4:50m

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