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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

(8 - 8 x)^{2}

\frac{625000 ( 3 + 2 e ^{10} )}{7 e ^{5}}

(1 + e^{- x}) e^{x}

5 \cdot (x + 7 + 149) (x + 7 - 149)

\frac{- x + 1}{( x + 1 ) ^{3}}

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