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Popular >

derivative of y^2cos(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = y^{2}, g = cos (x)

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

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

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

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

Simplify

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

Popular Examples

(\partial)/(\partial x)(sqrt(25+x^2))

\frac{\partial}{\partial x} (25 + x^{2})

(dy)/(dx)-2y=x^2+5

\frac{d y}{d x} - 2 y = x^{2} + 5

2y(dy)/(dx)= x/(sqrt(x^2-16))

2 y \frac{d y}{d x} = \frac{x}{x ^{2} - 16}

(\partial)/(\partial x)(4e^{xy}ln(x^2+y^2))

\frac{\partial}{\partial x} (4 e^{x y} ln (x^{2} + y^{2}))

integral of 1/(x^2+4x+4)

\int \frac{1}{x ^{2} + 4 x + 4} d x

Frequently Asked Questions (FAQ)

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