What is the derivative of (1/(y^2)-6/(y^4))(y+4y^3) ?

The derivative of (1/(y^2)-6/(y^4))(y+4y^3) is (23)/(y^2)+(18)/(y^4)+4

What is the first derivative of (1/(y^2)-6/(y^4))(y+4y^3) ?

The first derivative of (1/(y^2)-6/(y^4))(y+4y^3) is (23)/(y^2)+(18)/(y^4)+4

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derivative of

(\frac{1}{y ^{2}} - \frac{6}{y ^{4}}) (y + 4 y^{3})

\frac{23}{y ^{2}} + \frac{18}{y ^{4}} + 4

Solution steps

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{6}{y ^{4}}) (y + 4 y^{3}))

Apply the Product Rule:

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

f = \frac{1}{y ^{2}} - \frac{6}{y ^{4}}, g = y + 4 y^{3}

= \frac{d}{d y} (\frac{1}{y ^{2}} - \frac{6}{y ^{4}}) (y + 4 y^{3}) + \frac{d}{d y} (y + 4 y^{3}) (\frac{1}{y ^{2}} - \frac{6}{y ^{4}})

\frac{d}{d y} (\frac{1}{y ^{2}} - \frac{6}{y ^{4}}) = - \frac{2}{y ^{3}} + \frac{24}{y ^{5}}

\frac{d}{d y} (y + 4 y^{3}) = 1 + 12 y^{2}

= (- \frac{2}{y ^{3}} + \frac{24}{y ^{5}}) (y + 4 y^{3}) + (1 + 12 y^{2}) (\frac{1}{y ^{2}} - \frac{6}{y ^{4}})

Simplify

(- \frac{2}{y ^{3}} + \frac{24}{y ^{5}}) (y + 4 y^{3}) + (1 + 12 y^{2}) (\frac{1}{y ^{2}} - \frac{6}{y ^{4}}) : \frac{23}{y ^{2}} + \frac{18}{y ^{4}} + 4

= \frac{23}{y ^{2}} + \frac{18}{y ^{4}} + 4

x \to 3 lim (I n (x - 3))

(f (x))^{3}

y = x^{2} + 1, (- 1, 2)

\int u^{3} u^{4} + 2 d u

\frac{d}{d x} (e^{- x} ln (x))

What is the derivative of (1/(y^2)-6/(y^4))(y+4y^3) ?
The derivative of (1/(y^2)-6/(y^4))(y+4y^3) is (23)/(y^2)+(18)/(y^4)+4
What is the first derivative of (1/(y^2)-6/(y^4))(y+4y^3) ?
The first derivative of (1/(y^2)-6/(y^4))(y+4y^3) is (23)/(y^2)+(18)/(y^4)+4