What is the derivative of (x-2^3(6-x)^4) ?

The derivative of (x-2^3(6-x)^4) is 3(x-2)^2(6-x)^4-4(6-x)^3(x-2)^3

What is the first derivative of (x-2^3(6-x)^4) ?

The first derivative of (x-2^3(6-x)^4) is 3(x-2)^2(6-x)^4-4(6-x)^3(x-2)^3

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

3 (x - 2)^{2} (6 - x)^{4} - 4 (6 - x)^{3} (x - 2)^{3}

Solution steps

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

Apply the Product Rule:

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

f = (x - 2)^{3}, g = (6 - x)^{4}

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

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

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

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

Simplify

= 3 (x - 2)^{2} (6 - x)^{4} - 4 (6 - x)^{3} (x - 2)^{3}

\frac{d}{d x} (2^{x} sin (x))

\int cos (b + a x) d x

2 x^{2} y y^{^{'}} + 2 x y^{2} + 1 = 0

\int (4^{x}) d x

\frac{d}{d x} (3 ln (x + 1))

What is the derivative of (x-2^3(6-x)^4) ?
The derivative of (x-2^3(6-x)^4) is 3(x-2)^2(6-x)^4-4(6-x)^3(x-2)^3
What is the first derivative of (x-2^3(6-x)^4) ?
The first derivative of (x-2^3(6-x)^4) is 3(x-2)^2(6-x)^4-4(6-x)^3(x-2)^3