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

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

$7e^x+6x^2$

$7e^x+6x$

$7+6x^2$

$7e^x+2x^3$

Verified step by step guidance

Identify the function for which you need to find the derivative: $ g(x) = 7e^x + 2x^3 $.

Apply the sum rule of differentiation, which states that the derivative of a sum of functions is the sum of their derivatives. So, differentiate each term separately.

Differentiate the first term $ 7e^x $. The derivative of $ e^x $ is $ e^x $, so the derivative of $ 7e^x $ is $ 7e^x $.

Differentiate the second term $ 2x^3 $. Use the power rule, which states that the derivative of $ x^n $ is $ nx^{n-1} $. Therefore, the derivative of $ 2x^3 $ is $ 6x^2 $.

Combine the derivatives of the individual terms to get the derivative of the entire function: $ g'(x) = 7e^x + 6x^2 $.

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