What is the derivative of [x^2(x^2+5x)]^6 ?

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

What is the first derivative of [x^2(x^2+5x)]^6 ?

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

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derivative of

[x^{2} (x^{2} + 5 x)]^{6}

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

Solution steps

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

Simplify

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

= \frac{d}{d x} (x^{12} (x^{2} + 5 x)^{6})

Apply the Product Rule:

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

f = x^{12}, g = (x^{2} + 5 x)^{6}

= \frac{d}{d x} (x^{12}) (x^{2} + 5 x)^{6} + \frac{d}{d x} ((x^{2} + 5 x)^{6}) x^{12}

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

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

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

f (x) = y^{2} - x y

\int x^{2} (x - 2) d x

n = 0 \sum \infty \frac{n !}{10 3 ^{n}}

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

f (x) = x^{3} - \frac{3}{2} x^{2}

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