What is the derivative of 4x^4+x^3-(9x^2/2+8x) ?

The derivative of 4x^4+x^3-(9x^2/2+8x) is 16x^3+3x^2-9x+8

What is the first derivative of 4x^4+x^3-(9x^2/2+8x) ?

The first derivative of 4x^4+x^3-(9x^2/2+8x) is 16x^3+3x^2-9x+8

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\frac{d}{d x} (4 x^{4} + x^{3} - \frac{9 x ^{2}}{2} + 8 x)

16 x^{3} + 3 x^{2} - 9 x + 8

Solution steps

\frac{d}{d x} (4 x^{4} + x^{3} - \frac{9 x ^{2}}{2} + 8 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 x^{4}) + \frac{d}{d x} (x^{3}) - \frac{d}{d x} (\frac{9 x ^{2}}{2}) + \frac{d}{d x} (8 x)

\frac{d}{d x} (4 x^{4}) = 16 x^{3}

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

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

\frac{d}{d x} (8 x) = 8

= 16 x^{3} + 3 x^{2} - 9 x + 8

What is the derivative of 4x^4+x^3-(9x^2/2+8x) ?
The derivative of 4x^4+x^3-(9x^2/2+8x) is 16x^3+3x^2-9x+8
What is the first derivative of 4x^4+x^3-(9x^2/2+8x) ?
The first derivative of 4x^4+x^3-(9x^2/2+8x) is 16x^3+3x^2-9x+8