What is the derivative of y=(pi^2x^6+9000)/(x^2) ?

The derivative of y=(pi^2x^6+9000)/(x^2) is (4(pi^2x^6-4500))/(x^3)

What is the first derivative of y=(pi^2x^6+9000)/(x^2) ?

The first derivative of y=(pi^2x^6+9000)/(x^2) is (4(pi^2x^6-4500))/(x^3)

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derivative of

y = \frac{π ^{2} x ^{6} + 9000}{x ^{2}}

\frac{4 ( π ^{2} x ^{6} - 4500 )}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{π ^{2} x ^{6} + 9000}{x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( π ^{2} x ^{6} + 9000 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( π ^{2} x ^{6} + 9000 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (π^{2} x^{6} + 9000) = 6 π^{2} x^{5}

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

= \frac{6 π ^{2} x ^{5} x ^{2} - 2 x ( π ^{2} x ^{6} + 9000 )}{( x ^{2} ) ^{2}}

Simplify

\frac{6 π ^{2} x ^{5} x ^{2} - 2 x ( π ^{2} x ^{6} + 9000 )}{( x ^{2} ) ^{2}} : \frac{4 ( π ^{2} x ^{6} - 4500 )}{x ^{3}}

= \frac{4 ( π ^{2} x ^{6} - 4500 )}{x ^{3}}

\int 2 tan^{4} (x se) c^{6} x d x

f (x) = e^{x}, at x = 7

\frac{d}{d x} (\frac{3 x + 5}{1 + x})

\frac{d}{d x} (3^{x} \cdot ln (3))

\int_{4}^{\infty} e^{- \frac{x}{5}} d x

What is the derivative of y=(pi^2x^6+9000)/(x^2) ?
The derivative of y=(pi^2x^6+9000)/(x^2) is (4(pi^2x^6-4500))/(x^3)
What is the first derivative of y=(pi^2x^6+9000)/(x^2) ?
The first derivative of y=(pi^2x^6+9000)/(x^2) is (4(pi^2x^6-4500))/(x^3)