What is the derivative of (x^9-6xsqrt(x))/x ?

The derivative of (x^9-6xsqrt(x))/x is 8x^7-3/(sqrt(x))

What is the first derivative of (x^9-6xsqrt(x))/x ?

The first derivative of (x^9-6xsqrt(x))/x is 8x^7-3/(sqrt(x))

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derivative of

\frac{x ^{9} - 6 x x}{x}

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

Solution steps

\frac{d}{d x} (\frac{x ^{9} - 6 x x}{x})

Simplify

\frac{x ^{9} - 6 x x}{x} : x^{8} - 6 x

= \frac{d}{d x} (x^{8} - 6 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{8}) - \frac{d}{d x} (6 x)

\frac{d}{d x} (x^{8}) = 8 x^{7}

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

= 8 x^{7} - \frac{3}{x}

\frac{d}{d x} (5^{x, x})

x^{5}

\int sin (t) 1 + cos (t) d t

9 e^{9 e^{x} + x}

\frac{d}{d x} (6 x + 6)

What is the derivative of (x^9-6xsqrt(x))/x ?
The derivative of (x^9-6xsqrt(x))/x is 8x^7-3/(sqrt(x))
What is the first derivative of (x^9-6xsqrt(x))/x ?
The first derivative of (x^9-6xsqrt(x))/x is 8x^7-3/(sqrt(x))