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Popular >

derivative of (x^6-6sqrt(x))

Solution

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

Solution

\frac{13 x ^{6} - 6}{2 x}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{6} - 6, g = x

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

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

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

= 6 x^{5} x + \frac{1}{2 x} (x^{6} - 6)

Simplify

6 x^{5} x + \frac{1}{2 x} (x^{6} - 6) : \frac{13 x ^{6} - 6}{2 x}

= \frac{13 x ^{6} - 6}{2 x}

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Frequently Asked Questions (FAQ)

What is the derivative of (x^6-6sqrt(x)) ?
The derivative of (x^6-6sqrt(x)) is (13x^6-6)/(2sqrt(x))
What is the first derivative of (x^6-6sqrt(x)) ?
The first derivative of (x^6-6sqrt(x)) is (13x^6-6)/(2sqrt(x))