What is the derivative of 6sqrt(x^7) ?

The derivative of 6sqrt(x^7) is 21x^{5/2}

What is the first derivative of 6sqrt(x^7) ?

The first derivative of 6sqrt(x^7) is 21x^{5/2}

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\frac{d}{d x} (6 x^{7})

21 x^{\frac{5}{2}}

Solution steps

\frac{d}{d x} (6 x^{7})

Take the constant out:

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

= 6 \frac{d}{d x} (x^{7})

Apply radical rule:

n a^{m} = a^{\frac{m}{n}}

= 6 \frac{d}{d x} (x^{\frac{7}{2}})

Apply the Power Rule:

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

= 6 \cdot \frac{7}{2} x^{\frac{7}{2} - 1}

Simplify

6 \cdot \frac{7}{2} x^{\frac{7}{2} - 1} : 21 x^{\frac{5}{2}}

= 21 x^{\frac{5}{2}}

\frac{d}{d x} (3 a x + b x^{3})

\frac{\partial}{\partial x} (3 x^{2} + 5 x y - 7 y^{2} + 1)

\frac{d}{d x} (e^{x^{2} + 4})

\int x^{2} (6 - x^{3}) d x

\frac{d}{d x} (cos^{2} (2 x + 1))

What is the derivative of 6sqrt(x^7) ?
The derivative of 6sqrt(x^7) is 21x^{5/2}
What is the first derivative of 6sqrt(x^7) ?
The first derivative of 6sqrt(x^7) is 21x^{5/2}