What is the derivative of x^7sqrt(x^2-9x+9) ?

The derivative of x^7sqrt(x^2-9x+9) is (16x^8-135x^7+126x^6)/(2sqrt(x^2-9x+9))

What is the first derivative of x^7sqrt(x^2-9x+9) ?

The first derivative of x^7sqrt(x^2-9x+9) is (16x^8-135x^7+126x^6)/(2sqrt(x^2-9x+9))

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\frac{d}{d x} (x^{7} x^{2} - 9 x + 9)

\frac{16 x ^{8} - 135 x ^{7} + 126 x ^{6}}{2 x ^{2} - 9 x + 9}

Solution steps

\frac{d}{d x} (x^{7} x^{2} - 9 x + 9)

Apply the Product Rule:

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

f = x^{7}, g = x^{2} - 9 x + 9

= \frac{d}{d x} (x^{7}) x^{2} - 9 x + 9 + \frac{d}{d x} (x^{2} - 9 x + 9) x^{7}

\frac{d}{d x} (x^{7}) = 7 x^{6}

\frac{d}{d x} (x^{2} - 9 x + 9) = \frac{2 x - 9}{2 x ^{2} - 9 x + 9}

= 7 x^{6} x^{2} - 9 x + 9 + \frac{2 x - 9}{2 x ^{2} - 9 x + 9} x^{7}

Simplify

7 x^{6} x^{2} - 9 x + 9 + \frac{2 x - 9}{2 x ^{2} - 9 x + 9} x^{7} : \frac{16 x ^{8} - 135 x ^{7} + 126 x ^{6}}{2 x ^{2} - 9 x + 9}

= \frac{16 x ^{8} - 135 x ^{7} + 126 x ^{6}}{2 x ^{2} - 9 x + 9}

\frac{d}{d y} ((2 - x) (y - 2) (3 - x - y))

\int \frac{x + 1}{2 x + 1} d x

\int 5 sin^{2} (x) d x

\frac{d}{d x} (2 x^{2} - 5 x + 4)

100

What is the derivative of x^7sqrt(x^2-9x+9) ?
The derivative of x^7sqrt(x^2-9x+9) is (16x^8-135x^7+126x^6)/(2sqrt(x^2-9x+9))
What is the first derivative of x^7sqrt(x^2-9x+9) ?
The first derivative of x^7sqrt(x^2-9x+9) is (16x^8-135x^7+126x^6)/(2sqrt(x^2-9x+9))