What is (\partial)/(\partial x)(((7x+4))/(4y+1)) ?

The answer to (\partial)/(\partial x)(((7x+4))/(4y+1)) is 7/(4y+1)

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(\partial)/(\partial x)(((7x+4))/(4y+1))

\frac{\partial}{\partial x} (\frac{( 7 x + 4 )}{4 y + 1})

\frac{7}{4 y + 1}

Solution steps

\frac{\partial}{\partial x} (\frac{( 7 x + 4 )}{4 y + 1})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{4 y + 1} \frac{\partial}{\partial x} (7 x + 4)

Apply the Sum/Difference Rule:

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

= \frac{1}{4 y + 1} (\frac{\partial}{\partial x} (7 x) + \frac{\partial}{\partial x} (4))

\frac{\partial}{\partial x} (7 x) = 7

\frac{\partial}{\partial x} (4) = 0

= \frac{1}{4 y + 1} (7 + 0)

Simplify

\frac{1}{4 y + 1} (7 + 0) : \frac{7}{4 y + 1}

= \frac{7}{4 y + 1}

(e^{4 x})^{2}

y^{^{'}} + 2 y = 50 e^{- 10 t}

\frac{d}{d x} (\frac{- x}{x ^{2} + 1})

\frac{4}{s ^{2} ( s + 1 )}

y^{^{''}} + 7 y^{^{'}} + 10 y = 13 t e^{5 t}

What is (\partial)/(\partial x)(((7x+4))/(4y+1)) ?
The answer to (\partial)/(\partial x)(((7x+4))/(4y+1)) is 7/(4y+1)