What is the derivative of f(x)=(7x+4)/(x+70) ?

The derivative of f(x)=(7x+4)/(x+70) is (486)/((x+70)^2)

What is the first derivative of f(x)=(7x+4)/(x+70) ?

The first derivative of f(x)=(7x+4)/(x+70) is (486)/((x+70)^2)

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derivative of

f (x) = \frac{7 x + 4}{x + 70}

\frac{486}{( x + 70 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{7 x + 4}{x + 70})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 7 x + 4 ) ( x + 70 ) - \frac{d}{d x} ( x + 70 ) ( 7 x + 4 )}{( x + 70 ) ^{2}}

\frac{d}{d x} (7 x + 4) = 7

\frac{d}{d x} (x + 70) = 1

= \frac{7 ( x + 70 ) - 1 \cdot ( 7 x + 4 )}{( x + 70 ) ^{2}}

Simplify

\frac{7 ( x + 70 ) - 1 \cdot ( 7 x + 4 )}{( x + 70 ) ^{2}} : \frac{486}{( x + 70 ) ^{2}}

= \frac{486}{( x + 70 ) ^{2}}

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y^{^{''}} + x^{2} y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 2

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What is the derivative of f(x)=(7x+4)/(x+70) ?
The derivative of f(x)=(7x+4)/(x+70) is (486)/((x+70)^2)
What is the first derivative of f(x)=(7x+4)/(x+70) ?
The first derivative of f(x)=(7x+4)/(x+70) is (486)/((x+70)^2)