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Algebra of Derivatives

If y=2x3+3x...

Question

If $y = 2 x^{3} + \frac{3}{x^{2}}$ , then find $\frac{d y}{d x}$ .

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Solution

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

Differentiating w.r.t. x, we get,

$\frac{d y}{d x} = 6 x^{2} - 6 x^{- 3}$

$\frac{d y}{d x} = 6 x^{2} - \frac{6}{x^{3}}$

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Similar questions

y = [2 x^{3} + 2] [2 x^{- 3} + 1]

\frac{d y}{d x}

y = 4 x^{4} + 2 x^{3} + \frac{5}{x} + 9

d y / d x

y = [\frac{x^{2} + 1}{x + 1}]

\frac{d y}{d x}

\frac{d y}{d x}

2 x^{3} + 2 y^{3} + x^{2} + y^{2} + 4 = sin x

Q. One of these six people has murdered one of the others. Each has made 3 statements. The murderer has made 3 errors. The victim has made zero errors. The other suspects have made one or two errors. Find out who the murderer is and who the victim is.
Catwoman says.
1) If

y = x^{5} t h e n \frac{d y}{d x} = 5 x^{4}

y = 2 x^{3} + 3 x^{5}, t h e n \frac{d y}{d x} = 6 x + 15 x^{4}

y = 2 x^{3},

then gradient is 6 at (2, 16)

Bane says
1) If

A = 4 π r^{2}, t h e n \frac{d A}{d r} = 8 π r

A = 4 x^{10} t h e n \frac{d y}{d x} = 40 x^{10}

A = 7 x, t h e n \frac{d y}{d x} = 7

Joker says
1) If

y = x^{5}, t h e n \frac{d y}{d x} = 5 x^{5}

y = \sqrt{x}, t h e n \frac{d y}{d x} = \frac{1}{2} x

y = 2 x^{2},

then the gradient is 6 at (3, 18)

Poison Ivy says
1) If

A = 4 π r^{2}, t h e n \frac{d A}{d r} = 8 r

A = 4 x^{10} t h e n \frac{d y}{d x} = 40 x^{11}

y = 7 x + 2, t h e n \frac{d y}{d x} = 7

The Scare crow says
If

y = 3 x^{11}, t h e n \frac{d y}{d x} = 33 x^{10}

y = 3 x^{2} + 6 x + 6, t h e n \frac{d y}{d x} = 6 x + 6

The gradient of

x^{2} + 3 x + 3 i s 9 w h e n x = 3

Harley Quinn say
The gradient of

y = x^{3} + x^{2} + 3 x i s 10 w h e n x = 2

y = 2 x^{3},

then gradient is 24 at (2, 16)
If

y = 2 x^{2},

then gradient is 12 at (3, 18)

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