Find the derivative of the given function.g(x)=7ex+2x3g(x)=7e^x+2x^3g(x)=7ex+2x3

7 e x + 6 x 2 7e^x+6x^2 7 e x + 6 x 2

Find the derivative of the given function. g ( x ) = 7 e x + 2 x 3 g(x)=7e^x+2x^3 g ( x ) = 7 e x + 2 x 3

Here, we wanna find the derivative of the function g of x equals 7e to the x plus 2x cubed. So to find this derivative here, g prime of x, since I have 2 functions being added together, I can just add their derivatives in order to get the derivative of this entire function. So taking a look at that first term, 7 e to the x, we know that the derivative of e to the x is just e to the x. And from our constant multiple rule, we know that having a constant there is just going to leave our constant in that derivative. So this is 7 times the derivative of e to the x, which is just e to the x. Then adding this together with the derivative of 2x cubed, we can apply the power rule here, pulling that 3 out front, multiplying by it, then decreasing that power by 1. This gives us 6x squared. So my derivative here, g prime of x, is 7e to the x plus 6x squared. I'll see you in the next one.

Find the derivative of the given function. g ( x ) = 7 e x + 2 x 3 g(x)=7e^x+2x^3 g ( x ) = 7 e x + 2 x 3

7 e x + 6 x 2 7e^x+6x^2 7 e x + 6 x 2

7 e x + 6 x 7e^x+6x 7 e x + 6 x

7 e x + 2 x 3 7e^x+2x^3 7 e x + 2 x 3

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.
$g(x)=7e^x+2x^3$

$7e^x+6x^2$

$7e^x+6x$

$7+6x^2$

$7e^x+2x^3$

Verified step by step guidance

Step 1: Identify the function to differentiate. The given function is g(x) = 7e^x + 2x^3.

Step 2: Recall the derivative rules. For e^x, the derivative is e^x. For x^n, the derivative is n*x^(n-1).

Step 3: Differentiate the first term, 7e^x. Using the constant multiple rule, the derivative is 7 * e^x.

Step 4: Differentiate the second term, 2x^3. Using the power rule, the derivative is 3 * 2 * x^(3-1), which simplifies to 6x^2.

Step 5: Combine the results from Step 3 and Step 4. The derivative of g(x) is g'(x) = 7e^x + 6x^2.

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