y=9x^{4}-7x³+8x²-\;8/x+\;{10}{x³} then \;dy/dx is

Correct Answer is : 36x3−21x2+16x+8x−2−30x−436x³-21x²+16x+8x^{-2}-30x^{-4}36x3−21x2+16x+8x−2−30x−4

36x³-21x²+16x+8x^{-2}-30x^{-4}

36x³-21x²+16x+8x^{-2}+30x^{-4}

36x³+21x²+16x+8x^{-2}+30x^{-4}

Correct Answer is : 36x3−21x2+16x+8x−2−30x−436x³-21x²+16x+8x^{-2}-30x^{-4}36x3−21x2+16x+8x−2−30x−4

Test Index

Differential Calculus

Question : 40 of 69

Marks: +1, -0

y=9x^{4}-7x^{3}+8x^{2}-\;\frac{8}{x}+\;\frac{10}{x^{3}}

\;\frac{dy}{dx}

Solution:

Concept:

Use the power rule:

\frac{d}{dx}(x^n) = n x^{n-1}

for each term.

Explanation:

Rewrite

y = 9x^4 - 7x^3 + 8x^2 - 8x^{-1} + 10x^{-3}

Differentiate term by term:

\frac{d}{dx}(9x^4) = 36x^3

\frac{d}{dx}(-7x^3) = -21x^2

\frac{d}{dx}(8x^2) = 16x

\frac{d}{dx}(-8x^{-1}) = 8x^{-2}

\frac{d}{dx}(10x^{-3}) = -30x^{-4}

Add them:

36x^3 - 21x^2 + 16x + 8x^{-2} - 30x^{-4}

Answer:

Option A:

36x^{3}-21x^{2}+16x+8x^{-2}-30x^{-4}

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