How to find the derivative of e^3㏑(x²)

1 answer:

7 0

$f(x)=e^{3\ln x^2}\\\\f'(x)=e^{3\ln x^2}\cdot\dfrac{3}{x^2}\cdot2x=e^{3\ln x^2}\cdot\dfrac{6}{x}=\dfrac{6e^{3\ln x^2}}{x}\\\\\\but\ e^{3\ln x^2}=e^{\ln (x^2)^3}=e^{\ln x^6}=x^6\ where\ x\neq0\\\\therefore\ f'(x)=6x^5$

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A parent made x cupcakes for each of the 109 students in the fourth grade. Which expression could be used to determine the total

larisa86 [58]

109x is the expression that could be used to determine the total number of cupcakes made given that a parent made x cupcakes for each of the 109 students in the fourth grade. This can be obtained by forming the algebraic expression for the given conditions.

<h3>Find the required expression:</h3>

Algebraic expression is made up of numbers, operations and variables.

Algebraic expression is true for all values of x.

For example, 2x, 5x + 9 etc.

Given that,

A parent made x cupcakes for each of the 109 students in the fourth grade.

The total number of students in the class = 109

The number of cupcakes one student gets = 1 × x = x

⇒ The number of cupcakes 109 student gets = 109 × x = 109x

Hence 109x is the expression that could be used to determine the total number of cupcakes made given that a parent made x cupcakes for each of the 109 students in the fourth grade.

Learn more about algebraic expression here:

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Translate into an algebraic expression: n−1 increased by 110%

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