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Popular Calculus >

derivative of x^4-4x^3+4x^2

Solution

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

Solution

4 x^{3} - 12 x^{2} + 8 x

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (4 x^{2}) = 8 x

= 4 x^{3} - 12 x^{2} + 8 x

Graph

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y^{''}-4y^'-5y=-3e^4t,y(0)=0,y^'(0)=0

y^{^{''}} - 4 y^{^{'}} - 5 y = - 3 e^{4} t, y (0) = 0, y^{^{'}} (0) = 0

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Frequently Asked Questions (FAQ)

What is the derivative of x^4-4x^3+4x^2 ?
The derivative of x^4-4x^3+4x^2 is 4x^3-12x^2+8x
What is the first derivative of x^4-4x^3+4x^2 ?
The first derivative of x^4-4x^3+4x^2 is 4x^3-12x^2+8x