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Popular >

derivative of sin(x^3+y^2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Popular Examples

(\partial)/(\partial x)(1/((x+y)))

\frac{\partial}{\partial x} (\frac{1}{( x + y )})

integral of 4t^4e^{6t^5}

\int 4 t^{4} e^{6 t^{5}} d t

limit as n approaches infinity of (1)^n

n \to \infty lim ((1)^{n})

limit as x approaches-3 of sqrt(7x+22)

x \to - 3 lim (7 x + 22)

(dy)/(dx)(x+y)=x-y

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

Frequently Asked Questions (FAQ)

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