What is the derivative of (1+sqrt(x)/(x^4)) ?

The derivative of (1+sqrt(x)/(x^4)) is (x^{7/2}-8x^3(1+sqrt(x)))/(2x^8)

What is the first derivative of (1+sqrt(x)/(x^4)) ?

The first derivative of (1+sqrt(x)/(x^4)) is (x^{7/2}-8x^3(1+sqrt(x)))/(2x^8)

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\frac{d}{d x} (\frac{1 + x}{x ^{4}})

\frac{x ^{\frac{7}{2}} - 8 x ^{3} ( 1 + x )}{2 x ^{8}}

Solution steps

\frac{d}{d x} (\frac{1 + x}{x ^{4}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 1 + x ) x ^{4} - \frac{d}{d x} ( x ^{4} ) ( 1 + x )}{( x ^{4} ) ^{2}}

\frac{d}{d x} (1 + x) = \frac{1}{2 x}

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

= \frac{\frac{1}{2 x} x ^{4} - 4 x ^{3} ( 1 + x )}{( x ^{4} ) ^{2}}

Simplify

\frac{\frac{1}{2 x} x ^{4} - 4 x ^{3} ( 1 + x )}{( x ^{4} ) ^{2}} : \frac{x ^{\frac{7}{2}} - 8 x ^{3} ( 1 + x )}{2 x ^{8}}

= \frac{x ^{\frac{7}{2}} - 8 x ^{3} ( 1 + x )}{2 x ^{8}}

\frac{\partial}{\partial x} (5 y^{4} cos (3 x))

\frac{d}{d x} (\frac{4 x ^{3} + 6}{x})

\int_{25}^{50} 15 d x

\frac{d}{d x} (3 e^{x} + ln (x) + tan (x))

t \to 0 lim (\frac{7}{t} - \frac{7}{t ^{2} + t})

What is the derivative of (1+sqrt(x)/(x^4)) ?
The derivative of (1+sqrt(x)/(x^4)) is (x^{7/2}-8x^3(1+sqrt(x)))/(2x^8)
What is the first derivative of (1+sqrt(x)/(x^4)) ?
The first derivative of (1+sqrt(x)/(x^4)) is (x^{7/2}-8x^3(1+sqrt(x)))/(2x^8)