What is the derivative of (x-2^3(x^2+9)^4) ?

The derivative of (x-2^3(x^2+9)^4) is 3(x-2)^2(x^2+9)^4+8x(x^2+9)^3(x-2)^3

What is the first derivative of (x-2^3(x^2+9)^4) ?

The first derivative of (x-2^3(x^2+9)^4) is 3(x-2)^2(x^2+9)^4+8x(x^2+9)^3(x-2)^3

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\frac{d}{d x} ((x - 2)^{3} (x^{2} + 9)^{4})

3 (x - 2)^{2} (x^{2} + 9)^{4} + 8 x (x^{2} + 9)^{3} (x - 2)^{3}

Solution steps

\frac{d}{d x} ((x - 2)^{3} (x^{2} + 9)^{4})

Apply the Product Rule:

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

f = (x - 2)^{3}, g = (x^{2} + 9)^{4}

= \frac{d}{d x} ((x - 2)^{3}) (x^{2} + 9)^{4} + \frac{d}{d x} ((x^{2} + 9)^{4}) (x - 2)^{3}

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

\frac{d}{d x} ((x^{2} + 9)^{4}) = 8 x (x^{2} + 9)^{3}

= 3 (x - 2)^{2} (x^{2} + 9)^{4} + 8 x (x^{2} + 9)^{3} (x - 2)^{3}

What is the derivative of (x-2^3(x^2+9)^4) ?
The derivative of (x-2^3(x^2+9)^4) is 3(x-2)^2(x^2+9)^4+8x(x^2+9)^3(x-2)^3
What is the first derivative of (x-2^3(x^2+9)^4) ?
The first derivative of (x-2^3(x^2+9)^4) is 3(x-2)^2(x^2+9)^4+8x(x^2+9)^3(x-2)^3