What is the derivative of 1/2+3/32 (4x-(x^3/3)) ?

The derivative of 1/2+3/32 (4x-(x^3/3)) is -(3x^2)/(32)+3/8

What is the first derivative of 1/2+3/32 (4x-(x^3/3)) ?

The first derivative of 1/2+3/32 (4x-(x^3/3)) is -(3x^2)/(32)+3/8

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\frac{d}{d x} (\frac{1}{2} + \frac{3}{32} (4 x - \frac{x ^{3}}{3}))

- \frac{3 x ^{2}}{32} + \frac{3}{8}

Solution steps

\frac{d}{d x} (\frac{1}{2} + \frac{3}{32} (4 x - \frac{x ^{3}}{3}))

Simplify

\frac{1}{2} + \frac{3}{32} (4 x - \frac{x ^{3}}{3}) : \frac{1}{2} + \frac{3 x}{8} - \frac{x ^{3}}{32}

= \frac{d}{d x} (\frac{1}{2} + \frac{3 x}{8} - \frac{x ^{3}}{32})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{1}{2}) + \frac{d}{d x} (\frac{3 x}{8}) - \frac{d}{d x} (\frac{x ^{3}}{32})

\frac{d}{d x} (\frac{1}{2}) = 0

\frac{d}{d x} (\frac{3 x}{8}) = \frac{3}{8}

\frac{d}{d x} (\frac{x ^{3}}{32}) = \frac{3 x ^{2}}{32}

= 0 + \frac{3}{8} - \frac{3 x ^{2}}{32}

Simplify

= - \frac{3 x ^{2}}{32} + \frac{3}{8}

\frac{d}{d θ} (6 sin (θ))

y^{^{''}} - 2 y^{^{'}} + 8 y = 0

\frac{d y}{d x} = 32 x^{2} y^{3}

\frac{d}{d x} (\frac{7}{4 4 x ^{3}})

f (x) = \frac{( 13 x + 100 )}{x}

What is the derivative of 1/2+3/32 (4x-(x^3/3)) ?
The derivative of 1/2+3/32 (4x-(x^3/3)) is -(3x^2)/(32)+3/8
What is the first derivative of 1/2+3/32 (4x-(x^3/3)) ?
The first derivative of 1/2+3/32 (4x-(x^3/3)) is -(3x^2)/(32)+3/8