What is the derivative of 7x^{3/2} ?

The derivative of 7x^{3/2} is (21x^{1/2})/2

What is the first derivative of 7x^{3/2} ?

The first derivative of 7x^{3/2} is (21x^{1/2})/2

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\frac{d}{d x} (7 x^{\frac{3}{2}})

\frac{21 x ^{\frac{1}{2}}}{2}

Solution steps

\frac{d}{d x} (7 x^{\frac{3}{2}})

Take the constant out:

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

= 7 \frac{d}{d x} (x^{\frac{3}{2}})

Apply the Power Rule:

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

= 7 \cdot \frac{3}{2} x^{\frac{3}{2} - 1}

Simplify

7 \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : \frac{21 x ^{\frac{1}{2}}}{2}

= \frac{21 x ^{\frac{1}{2}}}{2}

\int \frac{x}{x ln ( x )} d x

y^{^{'}} = - y^{2} t - y^{2} t^{2}, y (0) = 3

\int sin (6 x) sin (5 x) d x

x \to \frac{1}{2} - lim (\frac{1}{2 x - 1})

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

What is the derivative of 7x^{3/2} ?
The derivative of 7x^{3/2} is (21x^{1/2})/2
What is the first derivative of 7x^{3/2} ?
The first derivative of 7x^{3/2} is (21x^{1/2})/2