What is the derivative of ({P}(x)(x(36-x)^2)) ?

The derivative of ({P}(x)(x(36-x)^2)) is derivative of {P}(x)x(36-x)^2+(3x^2-144x+1296){P}(x)

What is the first derivative of ({P}(x)(x(36-x)^2)) ?

The first derivative of ({P}(x)(x(36-x)^2)) is derivative of {P}(x)x(36-x)^2+(3x^2-144x+1296){P}(x)

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\frac{d}{d x} ((P (x)) (x (36 - x)^{2}))

\frac{d}{d x} (P (x)) x (36 - x)^{2} + (3 x^{2} - 144 x + 1296) P (x)

Solution steps

\frac{d}{d x} ((P (x)) (x (36 - x)^{2}))

Apply the Product Rule:

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

f = P (x), g = x (36 - x)^{2}

= \frac{d}{d x} (P (x)) x (36 - x)^{2} + \frac{d}{d x} (x (36 - x)^{2}) P (x)

\frac{d}{d x} (x (36 - x)^{2}) = 3 x^{2} - 144 x + 1296

= \frac{d}{d x} (P (x)) x (36 - x)^{2} + (3 x^{2} - 144 x + 1296) P (x)

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

\frac{( a - 3 ) ( - 2 - a )}{4}

(3 - 1) + (3 - 1) i

(- 2) - (1 - i) (\frac{1 + i}{2 - 2})

What is the derivative of ({P}(x)(x(36-x)^2)) ?
The derivative of ({P}(x)(x(36-x)^2)) is derivative of {P}(x)x(36-x)^2+(3x^2-144x+1296){P}(x)
What is the first derivative of ({P}(x)(x(36-x)^2)) ?
The first derivative of ({P}(x)(x(36-x)^2)) is derivative of {P}(x)x(36-x)^2+(3x^2-144x+1296){P}(x)