What is the first derivative of x^6 ?

The first derivative of x^6 is 6x^5

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derivative of x^6

\frac{d}{d x} (x^{6})

6 x^{5}

Solution steps

\frac{d}{d x} (x^{6})

Apply the Power Rule:

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

= 6 x^{6 - 1}

Simplify

= 6 x^{5}

5 y^{^{''}} + y^{^{'}} = - 2 x, y (0) = 0, y^{^{'}} (0) = - 15

\frac{d}{d x} (\frac{1}{e ^{2 x}})

(x + \frac{1}{3 x})^{2}

y = 6 x + x^{2}

\int \frac{1}{t ^{2} 6 - t ^{2}} d t