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

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

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

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

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derivative of

[x^{2} (x^{2} + 6 x)]^{6}

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

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

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

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

\int \frac{( x ^{2} - x + 12 )}{x ^{3} + 3 x} d x

4 v^{2} - 2

x \to 0 lim (\frac{1}{x} sin (\frac{1}{x}))

\int 18 cos^{2} (x) sin (x) d x

x \to 0 lim (\frac{3 - 5 x}{4 x})

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