What is the derivative of x^6sqrt(5x^2-x) ?

The derivative of x^6sqrt(5x^2-x) is (70x^7-13x^6)/(2sqrt(5x^2-x))

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

The first derivative of x^6sqrt(5x^2-x) is (70x^7-13x^6)/(2sqrt(5x^2-x))

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\frac{d}{d x} (x^{6} 5 x^{2} - x)

\frac{70 x ^{7} - 13 x ^{6}}{2 5 x ^{2} - x}

Solution steps

\frac{d}{d x} (x^{6} 5 x^{2} - x)

Apply the Product Rule:

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

f = x^{6}, g = 5 x^{2} - x

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

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

\frac{d}{d x} (5 x^{2} - x) = \frac{10 x - 1}{2 5 x ^{2} - x}

= 6 x^{5} 5 x^{2} - x + \frac{10 x - 1}{2 5 x ^{2} - x} x^{6}

Simplify

6 x^{5} 5 x^{2} - x + \frac{10 x - 1}{2 5 x ^{2} - x} x^{6} : \frac{70 x ^{7} - 13 x ^{6}}{2 5 x ^{2} - x}

= \frac{70 x ^{7} - 13 x ^{6}}{2 5 x ^{2} - x}

y = \frac{5}{1 + x ^{2}}, (5, 0.19231)

\int 9 e^{4 x + e^{4 x}} d x

\int \frac{ln ( x )}{( x - 1 ) ^{2}} d x

y = 12 x, (1, 12)

\int sin (x) d x

What is the derivative of x^6sqrt(5x^2-x) ?
The derivative of x^6sqrt(5x^2-x) is (70x^7-13x^6)/(2sqrt(5x^2-x))
What is the first derivative of x^6sqrt(5x^2-x) ?
The first derivative of x^6sqrt(5x^2-x) is (70x^7-13x^6)/(2sqrt(5x^2-x))