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

The derivative of f(x)=3x^3sqrt(x) is (21x^{5/2})/2

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

The first derivative of f(x)=3x^3sqrt(x) is (21x^{5/2})/2

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derivative of

f (x) = 3 x^{3} x

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

Solution steps

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

Simplify

3 x^{3} x : 3 x^{\frac{7}{2}}

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

x y^{^{'}} + 6 y = x^{3} - x

\frac{d y}{d x}, 3 x^{2} y^{3} = 3 x - 2 y^{2} - 16

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

\int \frac{e ^{u}}{( 5 - e ^{u} ) ^{2}} d u

\int \frac{x ^{2} - 25}{x ^{3}} d x

What is the derivative of f(x)=3x^3sqrt(x) ?
The derivative of f(x)=3x^3sqrt(x) is (21x^{5/2})/2
What is the first derivative of f(x)=3x^3sqrt(x) ?
The first derivative of f(x)=3x^3sqrt(x) is (21x^{5/2})/2