en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sin(y+xy-x^3)

Solution

\frac{d}{d x} (sin (y) + x y - x^{3})

Solution

cos (y) \frac{d y}{d x} + y + x \frac{d y}{d x} - 3 x^{2}

Solution steps

\frac{d}{d x} (sin (y) + x y - x^{3})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sin (y)) + \frac{d}{d x} (x y) - \frac{d}{d x} (x^{3})

\frac{d}{d x} (sin (y)) = cos (y) \frac{d y}{d x}

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

= cos (y) \frac{d y}{d x} + y + x \frac{d y}{d x} - 3 x^{2}

Popular Examples

derivative of (x+1^{ln(x)})

\frac{d}{d x} ((x + 1)^{l n (x)})

y^{''}+2y^'=2x+7-e^{-2x}

y^{^{''}} + 2 y^{^{'}} = 2 x + 7 - e^{- 2 x}

integral from-1 to 1 of (x^2-1)^2

\int_{- 1}^{1} (x^{2} - 1)^{2} d x

integral of (sqrt(x)-1)/(sqrt(x))

\int \frac{x - 1}{x} d x

6 x y^{^{'}} + y = x^{4}

Frequently Asked Questions (FAQ)

What is the derivative of sin(y+xy-x^3) ?
The derivative of sin(y+xy-x^3) is cos(y)(dy)/(dx)+y+x(dy)/(dx)-3x^2
What is the first derivative of sin(y+xy-x^3) ?
The first derivative of sin(y+xy-x^3) is cos(y)(dy)/(dx)+y+x(dy)/(dx)-3x^2