What is the derivative of f(x)=70(4+0.1x+0.01x^2) ?

The derivative of f(x)=70(4+0.1x+0.01x^2) is 70(0.02x+0.1)

What is the first derivative of f(x)=70(4+0.1x+0.01x^2) ?

The first derivative of f(x)=70(4+0.1x+0.01x^2) is 70(0.02x+0.1)

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derivative of

f (x) = 70 (4 + 0.1 x + 0.01 x^{2})

70 (0.02 x + 0.1)

Solution steps

\frac{d}{d x} (70 (4 + 0.1 x + 0.01 x^{2}))

Take the constant out:

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

= 70 \frac{d}{d x} (4 + 0.1 x + 0.01 x^{2})

Apply the Sum/Difference Rule:

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

= 70 (\frac{d}{d x} (4) + \frac{d}{d x} (0.1 x) + \frac{d}{d x} (0.01 x^{2}))

\frac{d}{d x} (4) = 0

\frac{d}{d x} (0.1 x) = 0.1

\frac{d}{d x} (0.01 x^{2}) = 0.02 x

= 70 (0 + 0.1 + 0.02 x)

Simplify

= 70 (0.02 x + 0.1)

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What is the derivative of f(x)=70(4+0.1x+0.01x^2) ?
The derivative of f(x)=70(4+0.1x+0.01x^2) is 70(0.02x+0.1)
What is the first derivative of f(x)=70(4+0.1x+0.01x^2) ?
The first derivative of f(x)=70(4+0.1x+0.01x^2) is 70(0.02x+0.1)