What is the derivative of 7sqrt(x)(x^3-4sqrt(x)+5) ?

The derivative of 7sqrt(x)(x^3-4sqrt(x)+5) is 7((7x^3-4sqrt(x)+5)/(2sqrt(x))-2)

What is the first derivative of 7sqrt(x)(x^3-4sqrt(x)+5) ?

The first derivative of 7sqrt(x)(x^3-4sqrt(x)+5) is 7((7x^3-4sqrt(x)+5)/(2sqrt(x))-2)

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\frac{d}{d x} (7 x (x^{3} - 4 x + 5))

7 (\frac{7 x ^{3} - 4 x + 5}{2 x} - 2)

Solution steps

\frac{d}{d x} (7 x (x^{3} - 4 x + 5))

Take the constant out:

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

= 7 \frac{d}{d x} (x (x^{3} - 4 x + 5))

Apply the Product Rule:

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

f = x, g = x^{3} - 4 x + 5

= 7 (\frac{d}{d x} (x) (x^{3} - 4 x + 5) + \frac{d}{d x} (x^{3} - 4 x + 5) x)

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

\frac{d}{d x} (x^{3} - 4 x + 5) = 3 x^{2} - \frac{2}{x}

= 7 (\frac{1}{2 x} (x^{3} - 4 x + 5) + (3 x^{2} - \frac{2}{x}) x)

Simplify

7 (\frac{1}{2 x} (x^{3} - 4 x + 5) + (3 x^{2} - \frac{2}{x}) x) : 7 (\frac{7 x ^{3} - 4 x + 5}{2 x} - 2)

= 7 (\frac{7 x ^{3} - 4 x + 5}{2 x} - 2)

\int \frac{u ^{3}}{1 + u ^{2}} d u

\int π x d x

t \to + 0 lim (\frac{2 t}{tan ( t )})

x \to \infty lim (- x - 1)

\int \frac{1}{9 x ^{2} + 16} d x

What is the derivative of 7sqrt(x)(x^3-4sqrt(x)+5) ?
The derivative of 7sqrt(x)(x^3-4sqrt(x)+5) is 7((7x^3-4sqrt(x)+5)/(2sqrt(x))-2)
What is the first derivative of 7sqrt(x)(x^3-4sqrt(x)+5) ?
The first derivative of 7sqrt(x)(x^3-4sqrt(x)+5) is 7((7x^3-4sqrt(x)+5)/(2sqrt(x))-2)