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derivative of f(x)=x^2(x-2)^4

Solution

derivative of

f (x) = x^{2} (x - 2)^{4}

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

(dy)/(dx)= y/(x^2+1)

\frac{d y}{d x} = \frac{y}{x ^{2} + 1}

(\partial)/(\partial x)(1/(x^2+1))

\frac{\partial}{\partial x} (\frac{1}{x ^{2} + 1})

derivative of (-2x-y/(x+2y))

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laplacetransform g(t)=3+t^5+sin(pit)laplace transform

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Frequently Asked Questions (FAQ)

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