y=x^(2)tan(x) (dy)/(dx)=

Identify Function: Identify the function to differentiate. We are given the function y = x^2 * tan(x). We need to find the derivative of this function with respect to x, which is denoted as (dy)/(dx).Apply Product Rule: Apply the product rule for differentiation. The product rule states that the derivative of a product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function. In this case, our first function is u = x^2 and our second function is v = tan(x).Differentiate u = x^2: Differentiate the first function u = x^2 with respect to x. The derivative of x^2 with respect to x is 2x.Differentiate v = tan(x): Differentiate the second function v = tan(x) with respect to x. The derivative of tan(x) with respect to x is sec^2(x).Apply Product Rule with Derivatives: Apply the product rule using the derivatives from steps 3 and 4. Using the product rule, we have: (dy)/(dx) = (du)/(dx) * v + u * (dv)/(dx) Substituting the derivatives we found, we get: (dy)/(dx) = 2x * tan(x) + x^2 * sec^2(x)Simplify Expression: Simplify the expression if possible. The expression is already in its simplest form, so we do not need to simplify further. (dy)/(dx) = 2x * tan(x) + x^2 * sec^2(x)

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$y=x^{2}\tan(x)$ $\newline$ $\frac{dy}{dx}=$

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Algebra 2

Find the vertex of the transformed function

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y=x^{2}\tan(x)

\newline

\frac{dy}{dx}=

Identify Function: Identify the function to differentiate. $\newline$ We are given the function $y = x^2 \cdot \tan(x)$ . We need to find the derivative of this function with respect to $x$ , which is denoted as $\frac{dy}{dx}$ .
Apply Product Rule: Apply the product rule for differentiation. $\newline$ The product rule states that the derivative of a product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function. In this case, our first function is $u = x^2$ and our second function is $v = \tan(x)$ .
Differentiate $u = x^2$ : Differentiate the first function $u = x^2$ with respect to $x$ . The derivative of $x^2$ with respect to $x$ is $2x$ .
Differentiate $v = \tan(x)$ : Differentiate the second function $v = \tan(x)$ with respect to $x$ . The derivative of $\tan(x)$ with respect to $x$ is $\sec^2(x)$ .
Apply Product Rule with Derivatives: Apply the product rule using the derivatives from steps $3$ and $4$ . $\newline$ Using the product rule, we have: $\newline$ $\frac{dy}{dx} = \frac{du}{dx} \cdot v + u \cdot \frac{dv}{dx}$ $\newline$ Substituting the derivatives we found, we get: $\newline$ $\frac{dy}{dx} = 2x \cdot \tan(x) + x^2 \cdot \sec^2(x)$
Simplify Expression: Simplify the expression if possible. $\newline$ The expression is already in its simplest form, so we do not need to simplify further. $\newline$ $\frac{dy}{dx} = 2x \cdot \tan(x) + x^2 \cdot \sec^2(x)$