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Evaluate the derivative dy/dx = 10x4 + 16x3 - 3x2 + 6x - 5 at x=2.

May 4, 2026Mathematics

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Answer

\text{283}

5 steps

The given expression for $\frac{dy}{dx}$ is
$\frac{dy}{dx} = 10x^4 + 16x^3 - 3x^2 + 6x - 5$
Substitute $x=2$ into the expression.
$\frac{dy}{dx} \Big|_{x=2} = 10(2)^4 + 16(2)^3 - 3(2)^2 + 6(2) - 5$
Calculate the powers of 2.
$\frac{dy}{dx} \Big|_{x=2} = 10(16) + 16(8) - 3(4) + 6(2) - 5$
Perform the multiplications.
$\frac{dy}{dx} \Big|_{x=2} = 160 + 128 - 12 + 12 - 5$
Perform the additions and subtractions.
$\frac{dy}{dx} \Big|_{x=2} = 288 - 12 + 12 - 5$ $\frac{dy}{dx} \Big|_{x=2} = 276 + 12 - 5$ $\frac{dy}{dx} \Big|_{x=2} = 288 - 5$ $\frac{dy}{dx} \Big|_{x=2} = \boxed{\text{283}}$

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