If y = 6x³ + 2x^{-2} - x^{-3}, find dy/dx.

Correct Answer is : dydx=18x2−4x−3+3x−4dy/dx = 18x² - 4x^{-3} + 3x^{-4}dxdy=18x2−4x−3+3x−4

dy/dx = 15x² - 4x^{-2} - 3x^{-2}

dy/dx = 18x² - 4x^{-3} + 3x^{-4}

dy/dx = 12x² + 4x^{-1} - 3x^{-2}

Correct Answer is : dydx=18x2−4x−3+3x−4dy/dx = 18x² - 4x^{-3} + 3x^{-4}dxdy=18x2−4x−3+3x−4

Test Index

JAMB Mathematics 2019 Paper

Question : 24

Total: 73

y = 6x^3 + 2x^{-2} - x^{-3}

\frac{dy}{dx}

Solution:

Concept:

Apply the power rule of differentiation: if

y = ax^n

, then

\frac{dy}{dx} = nax^{n-1}

Explanation:

Given

y = 6x^3 + 2x^{-2} - x^{-3}

, differentiate each term separately.

For the first term,

6x^3

: multiply by 3 and reduce the power by 1, giving

18x^2

For the second term,

2x^{-2}

: multiply by

-2

and reduce the power, giving

-4x^{-3}

For the third term,

-x^{-3}

: multiply by

-3

, giving

+3x^{-4}

Combining these results:

\frac{dy}{dx} = 18x^2 - 4x^{-3} + 3x^{-4}

Answer:

\frac{dy}{dx} = 18x^2 - 4x^{-3} + 3x^{-4}

, which is option C.

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