What is the derivative of 10sqrt(6x^9+9x^6) ?

The derivative of 10sqrt(6x^9+9x^6) is (90sqrt(3)x^5(x^3+1))/(sqrt(x^6)\sqrt{2x^3+3)}

What is the first derivative of 10sqrt(6x^9+9x^6) ?

The first derivative of 10sqrt(6x^9+9x^6) is (90sqrt(3)x^5(x^3+1))/(sqrt(x^6)\sqrt{2x^3+3)}

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derivative of

10 6 x^{9} + 9 x^{6}

\frac{90 3 x ^{5} ( x ^{3} + 1 )}{x ^{6} 2 x ^{3} + 3}

Solution steps

\frac{d}{d x} (10 6 x^{9} + 9 x^{6})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \frac{d}{d x} (6 x^{9} + 9 x^{6})

Apply the chain rule:

\frac{1}{2 6 x ^{9} + 9 x ^{6}} \frac{d}{d x} (6 x^{9} + 9 x^{6})

= \frac{1}{2 6 x ^{9} + 9 x ^{6}} \frac{d}{d x} (6 x^{9} + 9 x^{6})

\frac{d}{d x} (6 x^{9} + 9 x^{6}) = 54 x^{8} + 54 x^{5}

= 10 \cdot \frac{1}{2 6 x ^{9} + 9 x ^{6}} (54 x^{8} + 54 x^{5})

Simplify

10 \cdot \frac{1}{2 6 x ^{9} + 9 x ^{6}} (54 x^{8} + 54 x^{5}) : \frac{90 3 x ^{5} ( x ^{3} + 1 )}{x ^{6} 2 x ^{3} + 3}

= \frac{90 3 x ^{5} ( x ^{3} + 1 )}{x ^{6} 2 x ^{3} + 3}

x \to 2 - lim (\frac{x ^{2}}{x ^{2} - 4})

\frac{\partial}{\partial y} (x e^{y} - y e^{x})

\frac{d y}{d x} = 2 y - x y^{2}

\int - \frac{5}{12 - 12 x ^{2}} d x

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

What is the derivative of 10sqrt(6x^9+9x^6) ?
The derivative of 10sqrt(6x^9+9x^6) is (90sqrt(3)x^5(x^3+1))/(sqrt(x^6)\sqrt{2x^3+3)}
What is the first derivative of 10sqrt(6x^9+9x^6) ?
The first derivative of 10sqrt(6x^9+9x^6) is (90sqrt(3)x^5(x^3+1))/(sqrt(x^6)\sqrt{2x^3+3)}