What is the derivative of (4x^3-7)/(x^4) ?

The derivative of (4x^3-7)/(x^4) is (4(-x^3+7))/(x^5)

What is the first derivative of (4x^3-7)/(x^4) ?

The first derivative of (4x^3-7)/(x^4) is (4(-x^3+7))/(x^5)

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derivative of

\frac{4 x ^{3} - 7}{x ^{4}}

\frac{4 ( - x ^{3} + 7 )}{x ^{5}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{3} - 7}{x ^{4}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x ^{3} - 7 ) x ^{4} - \frac{d}{d x} ( x ^{4} ) ( 4 x ^{3} - 7 )}{( x ^{4} ) ^{2}}

\frac{d}{d x} (4 x^{3} - 7) = 12 x^{2}

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{12 x ^{2} x ^{4} - 4 x ^{3} ( 4 x ^{3} - 7 )}{( x ^{4} ) ^{2}}

Simplify

\frac{12 x ^{2} x ^{4} - 4 x ^{3} ( 4 x ^{3} - 7 )}{( x ^{4} ) ^{2}} : \frac{4 ( - x ^{3} + 7 )}{x ^{5}}

= \frac{4 ( - x ^{3} + 7 )}{x ^{5}}

\frac{d}{d x} (x^{2} + x + 10)

f (x) = 100 x^{5}

\frac{5}{( s - 3 ) ^{3}}

\int x (x + 5)^{6} d x

\frac{\partial}{\partial x} (2 x y - e^{x})

What is the derivative of (4x^3-7)/(x^4) ?
The derivative of (4x^3-7)/(x^4) is (4(-x^3+7))/(x^5)
What is the first derivative of (4x^3-7)/(x^4) ?
The first derivative of (4x^3-7)/(x^4) is (4(-x^3+7))/(x^5)