What is the derivative of 1/4 (70x^2-8x^3) ?

The derivative of 1/4 (70x^2-8x^3) is x(-6x+35)

What is the first derivative of 1/4 (70x^2-8x^3) ?

The first derivative of 1/4 (70x^2-8x^3) is x(-6x+35)

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derivative of

\frac{1}{4} (70 x^{2} - 8 x^{3})

x (- 6 x + 35)

Solution steps

\frac{d}{d x} (\frac{1}{4} (70 x^{2} - 8 x^{3}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{4} \frac{d}{d x} (70 x^{2} - 8 x^{3})

Apply the Sum/Difference Rule:

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

= \frac{1}{4} (\frac{d}{d x} (70 x^{2}) - \frac{d}{d x} (8 x^{3}))

\frac{d}{d x} (70 x^{2}) = 140 x

\frac{d}{d x} (8 x^{3}) = 24 x^{2}

= \frac{1}{4} (140 x - 24 x^{2})

Simplify

\frac{1}{4} (140 x - 24 x^{2}) : x (- 6 x + 35)

= x (- 6 x + 35)

What is the derivative of 1/4 (70x^2-8x^3) ?
The derivative of 1/4 (70x^2-8x^3) is x(-6x+35)
What is the first derivative of 1/4 (70x^2-8x^3) ?
The first derivative of 1/4 (70x^2-8x^3) is x(-6x+35)