What is the derivative of (x^5-6xsqrt(x))/x ?

The derivative of (x^5-6xsqrt(x))/x is 4x^3-3/(sqrt(x))

What is the first derivative of (x^5-6xsqrt(x))/x ?

The first derivative of (x^5-6xsqrt(x))/x is 4x^3-3/(sqrt(x))

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derivative of

\frac{x ^{5} - 6 x x}{x}

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

Solution steps

\frac{d}{d x} (\frac{x ^{5} - 6 x x}{x})

Simplify

\frac{x ^{5} - 6 x x}{x} : x^{4} - 6 x

= \frac{d}{d x} (x^{4} - 6 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{4}) - \frac{d}{d x} (6 x)

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

\frac{d}{d x} (6 x) = \frac{3}{x}

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

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

\frac{d}{d x} (x - y)

\int sec (x) tan (x) - 3 e^{x} d x

\int_{0}^{5} \frac{w}{w - 2} d w

x \to 0 lim (3 x cos (x))

What is the derivative of (x^5-6xsqrt(x))/x ?
The derivative of (x^5-6xsqrt(x))/x is 4x^3-3/(sqrt(x))
What is the first derivative of (x^5-6xsqrt(x))/x ?
The first derivative of (x^5-6xsqrt(x))/x is 4x^3-3/(sqrt(x))