What is the derivative of 3x+x^2-3x^3-x^4 ?

The derivative of 3x+x^2-3x^3-x^4 is 3+2x-9x^2-4x^3

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

The first derivative of 3x+x^2-3x^3-x^4 is 3+2x-9x^2-4x^3

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

3 + 2 x - 9 x^{2} - 4 x^{3}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d}{d x} (3 x^{3}) = 9 x^{2}

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

= 3 + 2 x - 9 x^{2} - 4 x^{3}

What is the derivative of 3x+x^2-3x^3-x^4 ?
The derivative of 3x+x^2-3x^3-x^4 is 3+2x-9x^2-4x^3
What is the first derivative of 3x+x^2-3x^3-x^4 ?
The first derivative of 3x+x^2-3x^3-x^4 is 3+2x-9x^2-4x^3