What is the derivative of 3sqrt(x)(x^3-3sqrt(x)+2) ?

The derivative of 3sqrt(x)(x^3-3sqrt(x)+2) is 3(-3/2+(7x^3-3sqrt(x)+2)/(2sqrt(x)))

What is the first derivative of 3sqrt(x)(x^3-3sqrt(x)+2) ?

The first derivative of 3sqrt(x)(x^3-3sqrt(x)+2) is 3(-3/2+(7x^3-3sqrt(x)+2)/(2sqrt(x)))

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derivative of

3 x (x^{3} - 3 x + 2)

3 (- \frac{3}{2} + \frac{7 x ^{3} - 3 x + 2}{2 x})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{3} - 3 x + 2

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Simplify

3 (\frac{1}{2 x} (x^{3} - 3 x + 2) + (3 x^{2} - \frac{3}{2 x}) x) : 3 (- \frac{3}{2} + \frac{7 x ^{3} - 3 x + 2}{2 x})

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

\frac{d y}{d x} = (4 x^{4} - 7 x^{2} + 6)

\int e^{2 x} + e^{- 2 x} d x

h \to 0 lim (2.5 h^{2} + 6 h)

3 t + 2 e^{3 t}

\frac{\partial}{\partial x} ((sin (y)) u (x, π))

What is the derivative of 3sqrt(x)(x^3-3sqrt(x)+2) ?
The derivative of 3sqrt(x)(x^3-3sqrt(x)+2) is 3(-3/2+(7x^3-3sqrt(x)+2)/(2sqrt(x)))
What is the first derivative of 3sqrt(x)(x^3-3sqrt(x)+2) ?
The first derivative of 3sqrt(x)(x^3-3sqrt(x)+2) is 3(-3/2+(7x^3-3sqrt(x)+2)/(2sqrt(x)))