What is the derivative of 10x^4 ?

The derivative of 10x^4 is 40x^3

What is the first derivative of 10x^4 ?

The first derivative of 10x^4 is 40x^3

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\frac{d}{d x} (10 x^{4})

40 x^{3}

Solution steps

\frac{d}{d x} (10 x^{4})

Take the constant out:

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

= 10 \frac{d}{d x} (x^{4})

Apply the Power Rule:

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

= 10 \cdot 4 x^{4 - 1}

Simplify

= 40 x^{3}

f (x) = ln (x^{2} - 8 x + 16)

\frac{\partial}{\partial x} (cos^{2} (θ))

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

\frac{d y}{d x} = 6 x e^{y}

C (x) = - 9 x^{2} + 500 x + 110