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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

3 x (x^{3} - 7 x + 4)

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = x^{3} - 7 x + 4

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

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

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

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

Simplify

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

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

\int_{1}^{4} \frac{1}{x - 2} d x

\frac{d}{d x} f (x) = 10 x^{2} tan (x)

\int \frac{x}{3 - x ^{2}} d x

y^{^{'}} + (2 sin (x) cos (x)) y = e^{- s i n^{2} (x)}

n \to \infty lim (2 n 2^{n} + n^{2})

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