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For the following equation, evaluate
(dy)/(dx) when
x=2.

y=3x^(3)+4
Answer:

For the following equation, evaluate $\frac{d y}{d x}$ when $x=2$ . $\newline$ $y=3 x^{3}+4$ $\newline$ Answer:

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Evaluate an exponential function

Full solution

Q. For the following equation, evaluate

\frac{d y}{d x}

when

x=2

.

\newline

y=3 x^{3}+4

\newline

Answer:

Find Derivative: To find the derivative of $y$ with respect to $x$ , we need to differentiate the function $y=3x^{3}+4$ . Differentiate each term separately: The derivative of $3x^{3}$ with respect to $x$ is $3 \times 3x^{(3-1)} = 9x^{2}$ . The derivative of a constant, like $4$ , is $0$ . So, $\frac{dy}{dx} = 9x^{2} + 0$ , which simplifies to $\frac{dy}{dx} = 9x^{2}$ .
Differentiate Terms: Now we need to evaluate the derivative at $x=2$ . Substitute $x=2$ into the derivative to get $\frac{dy}{dx} = 9\cdot(2)^2$ . Calculate the value: $9\cdot(2)^2 = 9\cdot4 = 36$ .

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