What is the derivative of 3x^5sqrt(x) ?

The derivative of 3x^5sqrt(x) is (33x^{9/2})/2

What is the first derivative of 3x^5sqrt(x) ?

The first derivative of 3x^5sqrt(x) is (33x^{9/2})/2

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derivative of

3 x^{5} x

\frac{33 x ^{\frac{9}{2}}}{2}

Solution steps

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

Simplify

3 x^{5} x : 3 x^{\frac{11}{2}}

= \frac{d}{d x} (3 x^{\frac{11}{2}})

Take the constant out:

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

= 3 \frac{d}{d x} (x^{\frac{11}{2}})

Apply the Power Rule:

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

= 3 \cdot \frac{11}{2} x^{\frac{11}{2} - 1}

Simplify

3 \cdot \frac{11}{2} x^{\frac{11}{2} - 1} : \frac{33 x ^{\frac{9}{2}}}{2}

= \frac{33 x ^{\frac{9}{2}}}{2}

\frac{d}{d t} (2 + 4 t)

8 x y \frac{d y}{d x} = 1

\int cos^{3} (\frac{x}{16}) d x

n = 0 \sum \infty e^{- a \cdot n}

\int_{2}^{3} 20 x d x

What is the derivative of 3x^5sqrt(x) ?
The derivative of 3x^5sqrt(x) is (33x^{9/2})/2
What is the first derivative of 3x^5sqrt(x) ?
The first derivative of 3x^5sqrt(x) is (33x^{9/2})/2