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

The derivative of (x^6-5)sqrt(x) is (13x^6-5)/(2sqrt(x))

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

The first derivative of (x^6-5)sqrt(x) is (13x^6-5)/(2sqrt(x))

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derivative of

(x^{6} - 5) x

\frac{13 x ^{6} - 5}{2 x}

Solution steps

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

Apply the Product Rule:

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

f = x^{6} - 5, g = x

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

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

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

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

Simplify

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

= \frac{13 x ^{6} - 5}{2 x}

What is the derivative of (x^6-5)sqrt(x) ?
The derivative of (x^6-5)sqrt(x) is (13x^6-5)/(2sqrt(x))
What is the first derivative of (x^6-5)sqrt(x) ?
The first derivative of (x^6-5)sqrt(x) is (13x^6-5)/(2sqrt(x))