Question

Derivative of sqrt(4-3x^2)

Answer 1

just a quick addition to the reply by "evelynguzman83" above

`f(x)=√(4-3x^2)\implies f(x)= (4-3x^2)^{(1)/(2)}\implies \cfrac{df}{dx}=\stackrel{ \textit{chain rule} }{\cfrac{1}{2}(4-3x^2)^{-(1)/(2)}\cdot (-6x)} \\\\\\ \cfrac{df}{dx}=(4-3x^2)^{-(1)/(2)}\cdot (-3x)\implies \cfrac{df}{dx}=\cfrac{-3x}{√(4-3x^2)}`

Answer 2

~~~

Answer explanation:

The derivative of sqrt(4-3x^2) can be found using the chain rule. Let's break down the process step by step: 1. Start by identifying the outer function and the inner function. In this case, the outer function is the square root function (sqrt) and the inner function is (4-3x^2). 2. Next, differentiate the outer function with respect to the inner function. The derivative of sqrt(u) is 1 / (2 * sqrt(u)), where u represents the inner function. So, the derivative of sqrt(4-3x^2) with respect to (4-3x^2) is 1 / (2 * sqrt(4-3x^2)). 3. Finally, multiply the derivative of the outer function by the derivative of the inner function. The derivative of (4-3x^2) with respect to x is -6x. Putting it all together, the derivative of sqrt(4-3x^2) is: (1 / (2 * sqrt(4-3x^2))) * (-6x) Simplifying the expression gives us: -3x / sqrt(4-3x^2) So, the derivative of sqrt(4-3x^2) is -3x / sqrt(4-3x^2).