What is the derivative of \sqrt[3]{x^2}sin(5x) ?

The derivative of \sqrt[3]{x^2}sin(5x) is (2sin(5x))/(3x^{1/3)}+5cos(5x)\sqrt[3]{x^2}

What is the first derivative of \sqrt[3]{x^2}sin(5x) ?

The first derivative of \sqrt[3]{x^2}sin(5x) is (2sin(5x))/(3x^{1/3)}+5cos(5x)\sqrt[3]{x^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (3 x^{2} sin (5 x))

\frac{2 sin ( 5 x )}{3 x ^{\frac{1}{3}}} + 5 cos (5 x) 3 x^{2}

Solution steps

\frac{d}{d x} (3 x^{2} sin (5 x))

Apply the Product Rule:

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

f = 3 x^{2}, g = sin (5 x)

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

\frac{d}{d x} (3 x^{2}) = \frac{2}{3 x ^{\frac{1}{3}}}

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= \frac{2}{3 x ^{\frac{1}{3}}} sin (5 x) + cos (5 x) \cdot 5 3 x^{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 sin ( 5 x )}{3 x ^{\frac{1}{3}}} + 5 cos (5 x) 3 x^{2}

\frac{d}{d x} (arctanh (x))

\int 5 x ln (5 x) d x

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

y = (7 t - 4), (0, 0.5)

\frac{d}{d x} (x^{t a n (x)})

What is the derivative of \sqrt[3]{x^2}sin(5x) ?
The derivative of \sqrt[3]{x^2}sin(5x) is (2sin(5x))/(3x^{1/3)}+5cos(5x)\sqrt[3]{x^2}
What is the first derivative of \sqrt[3]{x^2}sin(5x) ?
The first derivative of \sqrt[3]{x^2}sin(5x) is (2sin(5x))/(3x^{1/3)}+5cos(5x)\sqrt[3]{x^2}