Let y=2e^(4x). Find (d^(2)y)/(dx^(2)). Choose 1 answer: (A) 40e^(6x) (B) 8e^(x) (C) 32e^(4x) (D) (e^(4x))/(8)

Find First Derivative: Differentiate the function y = 2e^(4x) with respect to x to find the first derivative. Using the chain rule, the derivative of e^(4x) is 4e^(4x), and since we have a constant 2 multiplied, the first derivative is: dy/dx = 2 * 4e^(4x) = 8e^(4x)Apply Chain Rule: Differentiate the first derivative to find the second derivative. Again using the chain rule, the derivative of 8e^(4x) is 8 * 4e^(4x), which gives us: d^2y/dx^2 = 8 * 4e^(4x) = 32e^(4x)

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Let
y=2e^(4x).
Find
(d^(2)y)/(dx^(2)).
Choose 1 answer:
(A)
40e^(6x)
(B)
8e^(x)
(C)
32e^(4x)
(D)
(e^(4x))/(8)

Let $y=2 e^{4 x}$ . $\newline$ Find $\frac{d^{2} y}{d x^{2}}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $40 e^{6 x}$ $\newline$ (B) $8 e^{x}$ $\newline$ (C) $32 e^{4 x}$ $\newline$ (D) $\frac{e^{4 x}}{8}$

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Math Problems

Algebra 2

Simplify rational expressions

Full solution

Q. Let

y=2 e^{4 x}

\newline

Find

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

\newline

Choose

1

answer:

\newline

(A)

40 e^{6 x}

\newline

(B)

8 e^{x}

\newline

(C)

32 e^{4 x}

\newline

(D)

\frac{e^{4 x}}{8}

Find First Derivative: Differentiate the function $y = 2e^{4x}$ with respect to $x$ to find the first derivative. $\newline$ Using the chain rule, the derivative of $e^{4x}$ is $4e^{4x}$ , and since we have a constant $2$ multiplied, the first derivative is: $\newline$ $\frac{dy}{dx} = 2 \times 4e^{4x} = 8e^{4x}$
Apply Chain Rule: Differentiate the first derivative to find the second derivative. $\newline$ Again using the chain rule, the derivative of $8e^{4x}$ is $8 \times 4e^{4x}$ , which gives us: $\newline$ $\frac{d^2y}{dx^2} = 8 \times 4e^{4x} = 32e^{4x}$