What is the derivative of (1/(y^2)-7/(y^4))(y+9y^3) ?

The derivative of (1/(y^2)-7/(y^4))(y+9y^3) is (62)/(y^2)+(21)/(y^4)+9

What is the first derivative of (1/(y^2)-7/(y^4))(y+9y^3) ?

The first derivative of (1/(y^2)-7/(y^4))(y+9y^3) is (62)/(y^2)+(21)/(y^4)+9

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derivative of

(\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y + 9 y^{3})

\frac{62}{y ^{2}} + \frac{21}{y ^{4}} + 9

Solution steps

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y + 9 y^{3}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{1}{y ^{2}} - \frac{7}{y ^{4}}, g = y + 9 y^{3}

= \frac{d}{d y} (\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y + 9 y^{3}) + \frac{d}{d y} (y + 9 y^{3}) (\frac{1}{y ^{2}} - \frac{7}{y ^{4}})

\frac{d}{d y} (\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) = - \frac{2}{y ^{3}} + \frac{28}{y ^{5}}

\frac{d}{d y} (y + 9 y^{3}) = 1 + 27 y^{2}

= (- \frac{2}{y ^{3}} + \frac{28}{y ^{5}}) (y + 9 y^{3}) + (1 + 27 y^{2}) (\frac{1}{y ^{2}} - \frac{7}{y ^{4}})

Simplify

(- \frac{2}{y ^{3}} + \frac{28}{y ^{5}}) (y + 9 y^{3}) + (1 + 27 y^{2}) (\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) : \frac{62}{y ^{2}} + \frac{21}{y ^{4}} + 9

= \frac{62}{y ^{2}} + \frac{21}{y ^{4}} + 9

x \to 3 lim (2 x - 3)

2 y^{^{''}} + 33 y = 0

x \to 1 lim (3 x)

k = 1 \sum \infty \frac{( - 1 ) ^{k}}{k}

\frac{d}{d x} ((6 x + 5)^{1.5})

What is the derivative of (1/(y^2)-7/(y^4))(y+9y^3) ?
The derivative of (1/(y^2)-7/(y^4))(y+9y^3) is (62)/(y^2)+(21)/(y^4)+9
What is the first derivative of (1/(y^2)-7/(y^4))(y+9y^3) ?
The first derivative of (1/(y^2)-7/(y^4))(y+9y^3) is (62)/(y^2)+(21)/(y^4)+9