What is the derivative of sqrt(x)cos(x^3) ?

The derivative of sqrt(x)cos(x^3) is (cos(x^3))/(2sqrt(x))-3x^2sqrt(x)sin(x^3)

What is the first derivative of sqrt(x)cos(x^3) ?

The first derivative of sqrt(x)cos(x^3) is (cos(x^3))/(2sqrt(x))-3x^2sqrt(x)sin(x^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (x cos (x^{3}))

\frac{cos ( x ^{3} )}{2 x} - 3 x^{2} x sin (x^{3})

Solution steps

\frac{d}{d x} (x cos (x^{3}))

Apply the Product Rule:

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

f = x, g = cos (x^{3})

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

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

\frac{d}{d x} (cos (x^{3})) = - sin (x^{3}) \cdot 3 x^{2}

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

Simplify

\frac{1}{2 x} cos (x^{3}) + (- sin (x^{3}) \cdot 3 x^{2}) x : \frac{cos ( x ^{3} )}{2 x} - 3 x^{2} x sin (x^{3})

= \frac{cos ( x ^{3} )}{2 x} - 3 x^{2} x sin (x^{3})

x \to 0 + lim ((\frac{1}{x})^{x})

sin (arccos (t))

\int \frac{1}{1 - 49 x ^{2}} d x

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

\int \frac{x}{x + 4} d x

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