What is the derivative of 5sqrt(x^5) ?

The derivative of 5sqrt(x^5) is (25x^{3/2})/2

What is the first derivative of 5sqrt(x^5) ?

The first derivative of 5sqrt(x^5) is (25x^{3/2})/2

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derivative of

5 x^{5}

\frac{25 x ^{\frac{3}{2}}}{2}

Solution steps

\frac{d}{d x} (5 x^{5})

Take the constant out:

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

= 5 \frac{d}{d x} (x^{5})

Apply radical rule:

= 5 \frac{d}{d x} (x^{\frac{5}{2}})

Apply the Power Rule:

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

= 5 \cdot \frac{5}{2} x^{\frac{5}{2} - 1}

Simplify

5 \cdot \frac{5}{2} x^{\frac{5}{2} - 1} : \frac{25 x ^{\frac{3}{2}}}{2}

= \frac{25 x ^{\frac{3}{2}}}{2}

\frac{d}{d t} (\frac{1}{t})

(6 x y - 2 y^{2}) d x + (3 x^{2} - 4 x y) d y = 0

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

\int \frac{10 x ^{2} - 9 x + 4}{x ( x ^{2} + 4 )} d x

2 x + 5, x^{2} + 2 x + 1

What is the derivative of 5sqrt(x^5) ?
The derivative of 5sqrt(x^5) is (25x^{3/2})/2
What is the first derivative of 5sqrt(x^5) ?
The first derivative of 5sqrt(x^5) is (25x^{3/2})/2