What is the first derivative of 20x^2 ?

The first derivative of 20x^2 is 40x

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derivative of 20x^2

\frac{d}{d x} (20 x^{2})

40 x

Solution steps

\frac{d}{d x} (20 x^{2})

Take the constant out:

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

= 20 \frac{d}{d x} (x^{2})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 20 \cdot 2 x^{2 - 1}

Simplify

= 40 x

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

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (0) = - 4, y^{^{'}} (0) = 21

\frac{d ^{2}}{d x ^{2}} (x (3 x + 2)^{5})

y = \frac{x}{x ^{2} + 5}

\frac{\partial}{\partial x} (1 - y)