What is the derivative of (4x^{3/2}-2x^{1/2}^3) ?

The derivative of (4x^{3/2}-2x^{1/2}^3) is (3(-1+6x)(4x^{3/2}-2x^{1/2})^2)/(x^{1/2)}

What is the first derivative of (4x^{3/2}-2x^{1/2}^3) ?

The first derivative of (4x^{3/2}-2x^{1/2}^3) is (3(-1+6x)(4x^{3/2}-2x^{1/2})^2)/(x^{1/2)}

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\frac{d}{d x} ((4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}})^{3})

\frac{3 ( - 1 + 6 x ) ( 4 x ^{\frac{3}{2}} - 2 x ^{\frac{1}{2}} ) ^{2}}{x ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} ((4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}})^{3})

Apply the chain rule:

3 (4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}})^{2} \frac{d}{d x} (4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}})

= 3 (4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}})^{2} \frac{d}{d x} (4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}})

\frac{d}{d x} (4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}}) = \frac{- 1 + 6 x}{x ^{\frac{1}{2}}}

= 3 (4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}})^{2} \frac{- 1 + 6 x}{x ^{\frac{1}{2}}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 ( - 1 + 6 x ) ( 4 x ^{\frac{3}{2}} - 2 x ^{\frac{1}{2}} ) ^{2}}{x ^{\frac{1}{2}}}

w (z) = 7 - z

10 y^{^{''}} + 11 y^{^{'}} = 5 cos (4 t)

\int tan (2 x) sec^{5} (2 x) d x

\frac{d}{d x} ((\frac{4}{5} x)^{4})

\int 4 sec^{2} (2 x) tan (2 x) d x

What is the derivative of (4x^{3/2}-2x^{1/2}^3) ?
The derivative of (4x^{3/2}-2x^{1/2}^3) is (3(-1+6x)(4x^{3/2}-2x^{1/2})^2)/(x^{1/2)}
What is the first derivative of (4x^{3/2}-2x^{1/2}^3) ?
The first derivative of (4x^{3/2}-2x^{1/2}^3) is (3(-1+6x)(4x^{3/2}-2x^{1/2})^2)/(x^{1/2)}