Let y=5cos(2x+10). Find (d^(2)y)/(dx^(2)). (d^(2)y)/(dx^(2))=

Find First Derivative: We are given the function y = 5cos(2x+10), and we need to find the second derivative of y with respect to x, which is denoted as (d^(2)y)/(dx^(2)). The first step is to find the first derivative of y with respect to x. Using the chain rule, the derivative of cos(u) with respect to x is -sin(u) * (du/dx), where u = 2x + 10 in this case. (dy/dx) = -sin(2x + 10) * d/dx(2x + 10) (dy/dx) = -sin(2x + 10) * 2Find Second Derivative: Now that we have the first derivative, we need to find the second derivative. We will differentiate -2sin(2x + 10) with respect to x. Using the chain rule again, the derivative of -sin(u) with respect to x is -cos(u) * (du/dx), where u = 2x + 10. (d^(2)y)/(dx^(2)) = -cos(2x + 10) * d/dx(2x + 10) (d^(2)y)/(dx^(2)) = -cos(2x + 10) * 2Simplify Expression: Simplify the expression for the second derivative. (d^(2)y)/(dx^(2)) = -2 * cos(2x + 10) * 2 (d^(2)y)/(dx^(2)) = -4cos(2x + 10)

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Algebra 2

Evaluate expression when two complex numbers are given

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Q. Let

y=5 \cos (2 x+10)

\newline

Find

\frac{d^{2} y}{d x^{2}}

\newline

\frac{d^{2} y}{d x^{2}}=

Find First Derivative: We are given the function $y = 5\cos(2x+10)$ , and we need to find the second derivative of $y$ with respect to $x$ , which is denoted as $\frac{d^{2}y}{dx^{2}}$ . The first step is to find the first derivative of $y$ with respect to $x$ . Using the chain rule, the derivative of $\cos(u)$ with respect to $x$ is $-\sin(u) \cdot \frac{du}{dx}$ , where $u = 2x + 10$ in this case. $y$ $0$ $y$ $1$
Find Second Derivative: Now that we have the first derivative, we need to find the second derivative. We will differentiate $-2\sin(2x + 10)$ with respect to $x$ . Using the chain rule again, the derivative of $-\sin(u)$ with respect to $x$ is $-\cos(u) \cdot (\frac{du}{dx})$ , where $u = 2x + 10$ . $\frac{d^2y}{dx^2} = -\cos(2x + 10) \cdot \frac{d}{dx}(2x + 10)$ $\frac{d^2y}{dx^2} = -\cos(2x + 10) \cdot 2$
Simplify Expression: Simplify the expression for the second derivative. $\newline$ $(d^{2}y)/(dx^{2}) = -2 \times \cos(2x + 10) \times 2$ $\newline$ $(d^{2}y)/(dx^{2}) = -4\cos(2x + 10)$