What is the derivative of [x^2(x^2+5x)]^4 ?

The derivative of [x^2(x^2+5x)]^4 is 8x^7(x^2+5x)^4+4(x^2+5x)^3(2x+5)x^8

What is the first derivative of [x^2(x^2+5x)]^4 ?

The first derivative of [x^2(x^2+5x)]^4 is 8x^7(x^2+5x)^4+4(x^2+5x)^3(2x+5)x^8

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derivative of

[x^{2} (x^{2} + 5 x)]^{4}

8 x^{7} (x^{2} + 5 x)^{4} + 4 (x^{2} + 5 x)^{3} (2 x + 5) x^{8}

Solution steps

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

Simplify

(x^{2} (x^{2} + 5 x))^{4} : x^{8} (x^{2} + 5 x)^{4}

= \frac{d}{d x} (x^{8} (x^{2} + 5 x)^{4})

Apply the Product Rule:

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

f = x^{8}, g = (x^{2} + 5 x)^{4}

= \frac{d}{d x} (x^{8}) (x^{2} + 5 x)^{4} + \frac{d}{d x} ((x^{2} + 5 x)^{4}) x^{8}

\frac{d}{d x} (x^{8}) = 8 x^{7}

\frac{d}{d x} ((x^{2} + 5 x)^{4}) = 4 (x^{2} + 5 x)^{3} (2 x + 5)

= 8 x^{7} (x^{2} + 5 x)^{4} + 4 (x^{2} + 5 x)^{3} (2 x + 5) x^{8}

e^{x^{4}}

x \to 3 lim ((x - 1)^{2})

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 0

x^{^{''}} + 9 x = 27, x (0) = 4, x^{^{'}} (0) = 6

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

What is the derivative of [x^2(x^2+5x)]^4 ?
The derivative of [x^2(x^2+5x)]^4 is 8x^7(x^2+5x)^4+4(x^2+5x)^3(2x+5)x^8
What is the first derivative of [x^2(x^2+5x)]^4 ?
The first derivative of [x^2(x^2+5x)]^4 is 8x^7(x^2+5x)^4+4(x^2+5x)^3(2x+5)x^8