What is the derivative of (x^4+48/(24x)) ?

The derivative of (x^4+48/(24x)) is (x^4-16)/(8x^2)

What is the first derivative of (x^4+48/(24x)) ?

The first derivative of (x^4+48/(24x)) is (x^4-16)/(8x^2)

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\frac{d}{d x} (\frac{x ^{4} + 48}{24 x})

\frac{x ^{4} - 16}{8 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{4} + 48}{24 x})

Take the constant out:

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

= \frac{1}{24} \frac{d}{d x} (\frac{x ^{4} + 48}{x})

Apply the Quotient Rule:

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

= \frac{1}{24} \cdot \frac{\frac{d}{d x} ( x ^{4} + 48 ) x - \frac{d x}{d x} ( x ^{4} + 48 )}{x ^{2}}

\frac{d}{d x} (x^{4} + 48) = 4 x^{3}

\frac{d x}{d x} = 1

= \frac{1}{24} \cdot \frac{4 x ^{3} x - 1 \cdot ( x ^{4} + 48 )}{x ^{2}}

Simplify

\frac{1}{24} \cdot \frac{4 x ^{3} x - 1 \cdot ( x ^{4} + 48 )}{x ^{2}} : \frac{x ^{4} - 16}{8 x ^{2}}

= \frac{x ^{4} - 16}{8 x ^{2}}

\frac{e ^{- π s}}{s}

x^{2} - 3 x, 3 x + 7, - 1, 7

\frac{d}{d t} (2^{t})

\int \frac{1}{y} e^{- \frac{x}{y}} d x

sin (x^{2})

What is the derivative of (x^4+48/(24x)) ?
The derivative of (x^4+48/(24x)) is (x^4-16)/(8x^2)
What is the first derivative of (x^4+48/(24x)) ?
The first derivative of (x^4+48/(24x)) is (x^4-16)/(8x^2)