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Popular >

derivative of (x-2^2(x-3)^3)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

integral of 3xsec^2(x)

\int 3 x sec^{2} (x) d x

integral of (sin^2(x))/(cos^6(x))

\int \frac{sin ^{2} ( x )}{cos ^{6} ( x )} d x

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\int x lo g_{10} (x) d x

limit as x approaches pi/4 of sin(x)

x \to \frac{π}{4} lim (sin (x))

f(x)= x/(3x+4ln(x))

f (x) = \frac{x}{3 x + 4 ln ( x )}

Frequently Asked Questions (FAQ)

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