What is the derivative of 7sqrt(x)(x^3-8sqrt(x)+2) ?

The derivative of 7sqrt(x)(x^3-8sqrt(x)+2) is 7((7x^3-8sqrt(x)+2)/(2sqrt(x))-4)

What is the first derivative of 7sqrt(x)(x^3-8sqrt(x)+2) ?

The first derivative of 7sqrt(x)(x^3-8sqrt(x)+2) is 7((7x^3-8sqrt(x)+2)/(2sqrt(x))-4)

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\frac{d}{d x} (7 x (x^{3} - 8 x + 2))

7 (\frac{7 x ^{3} - 8 x + 2}{2 x} - 4)

Solution steps

\frac{d}{d x} (7 x (x^{3} - 8 x + 2))

Take the constant out:

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

= 7 \frac{d}{d x} (x (x^{3} - 8 x + 2))

Apply the Product Rule:

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

f = x, g = x^{3} - 8 x + 2

= 7 (\frac{d}{d x} (x) (x^{3} - 8 x + 2) + \frac{d}{d x} (x^{3} - 8 x + 2) x)

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

\frac{d}{d x} (x^{3} - 8 x + 2) = 3 x^{2} - \frac{4}{x}

= 7 (\frac{1}{2 x} (x^{3} - 8 x + 2) + (3 x^{2} - \frac{4}{x}) x)

Simplify

7 (\frac{1}{2 x} (x^{3} - 8 x + 2) + (3 x^{2} - \frac{4}{x}) x) : 7 (\frac{7 x ^{3} - 8 x + 2}{2 x} - 4)

= 7 (\frac{7 x ^{3} - 8 x + 2}{2 x} - 4)

x \frac{d y}{d x} - 2 y = 5 x^{3}

\frac{\partial}{\partial x} (\frac{x ^{2}}{sin ^{2} ( x )})

\frac{\partial}{\partial z} (\frac{( x + y )}{y + z})

x \to 2 + lim (- \frac{5}{x - 2})

\int_{4}^{- 4} (- 7) d x

What is the derivative of 7sqrt(x)(x^3-8sqrt(x)+2) ?
The derivative of 7sqrt(x)(x^3-8sqrt(x)+2) is 7((7x^3-8sqrt(x)+2)/(2sqrt(x))-4)
What is the first derivative of 7sqrt(x)(x^3-8sqrt(x)+2) ?
The first derivative of 7sqrt(x)(x^3-8sqrt(x)+2) is 7((7x^3-8sqrt(x)+2)/(2sqrt(x))-4)