What is the derivative of (4x+9/x ^2) ?

The derivative of (4x+9/x ^2) is 32x-(162)/(x^3)

What is the first derivative of (4x+9/x ^2) ?

The first derivative of (4x+9/x ^2) is 32x-(162)/(x^3)

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\frac{d}{d x} ((4 x + \frac{9}{x})^{2})

32 x - \frac{162}{x ^{3}}

Solution steps

\frac{d}{d x} ((4 x + \frac{9}{x})^{2})

Simplify

(4 x + \frac{9}{x})^{2} : 16 x^{2} + 72 + \frac{81}{x ^{2}}

= \frac{d}{d x} (16 x^{2} + 72 + \frac{81}{x ^{2}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (16 x^{2}) + \frac{d}{d x} (72) + \frac{d}{d x} (\frac{81}{x ^{2}})

\frac{d}{d x} (16 x^{2}) = 32 x

\frac{d}{d x} (72) = 0

\frac{d}{d x} (\frac{81}{x ^{2}}) = - \frac{162}{x ^{3}}

= 32 x + 0 - \frac{162}{x ^{3}}

Simplify

= 32 x - \frac{162}{x ^{3}}

\frac{d}{d x} (e^{x} + e^{y})

\frac{d}{d x} (lo g_{10} (x^{2} + x + 1))

f (x) = \frac{2 x + 3}{3 x - 2}

\int_{0}^{2} \frac{1}{8 + 2 x ^{2}} d x

3 ln (x), x ln (x), 1, 2

What is the derivative of (4x+9/x ^2) ?
The derivative of (4x+9/x ^2) is 32x-(162)/(x^3)
What is the first derivative of (4x+9/x ^2) ?
The first derivative of (4x+9/x ^2) is 32x-(162)/(x^3)