What is the derivative of (x^2(x^2+9x))^6 ?

The derivative of (x^2(x^2+9x))^6 is 12x^{11}(x^2+9x)^6+6(x^2+9x)^5(2x+9)x^{12}

What is the first derivative of (x^2(x^2+9x))^6 ?

The first derivative of (x^2(x^2+9x))^6 is 12x^{11}(x^2+9x)^6+6(x^2+9x)^5(2x+9)x^{12}

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derivative of

(x^{2} (x^{2} + 9 x))^{6}

12 x^{11} (x^{2} + 9 x)^{6} + 6 (x^{2} + 9 x)^{5} (2 x + 9) x^{12}

Solution steps

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

Simplify

(x^{2} (x^{2} + 9 x))^{6} : x^{12} (x^{2} + 9 x)^{6}

= \frac{d}{d x} (x^{12} (x^{2} + 9 x)^{6})

Apply the Product Rule:

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

f = x^{12}, g = (x^{2} + 9 x)^{6}

= \frac{d}{d x} (x^{12}) (x^{2} + 9 x)^{6} + \frac{d}{d x} ((x^{2} + 9 x)^{6}) x^{12}

\frac{d}{d x} (x^{12}) = 12 x^{11}

\frac{d}{d x} ((x^{2} + 9 x)^{6}) = 6 (x^{2} + 9 x)^{5} (2 x + 9)

= 12 x^{11} (x^{2} + 9 x)^{6} + 6 (x^{2} + 9 x)^{5} (2 x + 9) x^{12}

\frac{\partial}{\partial x} (ln (x + y^{2}))

\frac{\partial}{\partial x} (\frac{2 x y}{x + y})

\int w w^{2} - ln (3) d w

x \to 0 lim (\frac{3 x}{x e ^{x}})

\int \frac{3 x ^{2} - 2 x + 5}{x ^{2}} d x

What is the derivative of (x^2(x^2+9x))^6 ?
The derivative of (x^2(x^2+9x))^6 is 12x^{11}(x^2+9x)^6+6(x^2+9x)^5(2x+9)x^{12}
What is the first derivative of (x^2(x^2+9x))^6 ?
The first derivative of (x^2(x^2+9x))^6 is 12x^{11}(x^2+9x)^6+6(x^2+9x)^5(2x+9)x^{12}