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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

= 7 \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

= 7 (\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}

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

Simplify

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

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

\int x^{2} (x + 3)^{2} d x

y = e^{- x}, y = 0, x = 0, x = ln (5)

x \to 3 lim (a x + 3)

y d x + (x^{2} - 4 x) d y = 0

n = 1 \sum \infty \frac{9 n}{n !}

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