What is the derivative of R(x)=[x^2(x^2+6x)]^4 ?

The derivative of R(x)=[x^2(x^2+6x)]^4 is 8x^7(x^2+6x)^4+4(x^2+6x)^3(2x+6)x^8

What is the first derivative of R(x)=[x^2(x^2+6x)]^4 ?

The first derivative of R(x)=[x^2(x^2+6x)]^4 is 8x^7(x^2+6x)^4+4(x^2+6x)^3(2x+6)x^8

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derivative of

R (x) = [x^{2} (x^{2} + 6 x)]^{4}

8 x^{7} (x^{2} + 6 x)^{4} + 4 (x^{2} + 6 x)^{3} (2 x + 6) x^{8}

Solution steps

\frac{d}{d x} ((x^{2} (x^{2} + 6 x))^{4})

Simplify

(x^{2} (x^{2} + 6 x))^{4} : x^{8} (x^{2} + 6 x)^{4}

= \frac{d}{d x} (x^{8} (x^{2} + 6 x)^{4})

Apply the Product Rule:

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

f = x^{8}, g = (x^{2} + 6 x)^{4}

= \frac{d}{d x} (x^{8}) (x^{2} + 6 x)^{4} + \frac{d}{d x} ((x^{2} + 6 x)^{4}) x^{8}

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

\frac{d}{d x} ((x^{2} + 6 x)^{4}) = 4 (x^{2} + 6 x)^{3} (2 x + 6)

= 8 x^{7} (x^{2} + 6 x)^{4} + 4 (x^{2} + 6 x)^{3} (2 x + 6) x^{8}

What is the derivative of R(x)=[x^2(x^2+6x)]^4 ?
The derivative of R(x)=[x^2(x^2+6x)]^4 is 8x^7(x^2+6x)^4+4(x^2+6x)^3(2x+6)x^8
What is the first derivative of R(x)=[x^2(x^2+6x)]^4 ?
The first derivative of R(x)=[x^2(x^2+6x)]^4 is 8x^7(x^2+6x)^4+4(x^2+6x)^3(2x+6)x^8