What is the derivative of (1/(y^2)-5/(y^4))(y+7y^3) ?

The derivative of (1/(y^2)-5/(y^4))(y+7y^3) is (34)/(y^2)+(15)/(y^4)+7

What is the first derivative of (1/(y^2)-5/(y^4))(y+7y^3) ?

The first derivative of (1/(y^2)-5/(y^4))(y+7y^3) is (34)/(y^2)+(15)/(y^4)+7

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derivative of

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

\frac{34}{y ^{2}} + \frac{15}{y ^{4}} + 7

Solution steps

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

Apply the Product Rule:

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

f = \frac{1}{y ^{2}} - \frac{5}{y ^{4}}, g = y + 7 y^{3}

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

\frac{d}{d y} (\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) = - \frac{2}{y ^{3}} + \frac{20}{y ^{5}}

\frac{d}{d y} (y + 7 y^{3}) = 1 + 21 y^{2}

= (- \frac{2}{y ^{3}} + \frac{20}{y ^{5}}) (y + 7 y^{3}) + (1 + 21 y^{2}) (\frac{1}{y ^{2}} - \frac{5}{y ^{4}})

Simplify

(- \frac{2}{y ^{3}} + \frac{20}{y ^{5}}) (y + 7 y^{3}) + (1 + 21 y^{2}) (\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) : \frac{34}{y ^{2}} + \frac{15}{y ^{4}} + 7

= \frac{34}{y ^{2}} + \frac{15}{y ^{4}} + 7

\frac{\partial}{\partial x} (\frac{x ^{α} y ^{β}}{y ^{1 - α} x ^{1 - β}})

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

sin (t^{2}) \cdot ln (t^{3})

\frac{\partial}{\partial x} ((1 + \frac{2}{y}) sin (x))

\frac{\partial}{\partial y} ((\frac{x}{y})^{\frac{1}{2}})

What is the derivative of (1/(y^2)-5/(y^4))(y+7y^3) ?
The derivative of (1/(y^2)-5/(y^4))(y+7y^3) is (34)/(y^2)+(15)/(y^4)+7
What is the first derivative of (1/(y^2)-5/(y^4))(y+7y^3) ?
The first derivative of (1/(y^2)-5/(y^4))(y+7y^3) is (34)/(y^2)+(15)/(y^4)+7