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Popular >

derivative of y^2-2ycos(x)

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

area y=10x^4-10x^2,y=9x^2 area

y = 10 x^{4} - 10 x^{2}, y = 9 x^{2}

integral of sqrt(1+(cos(x))^2)

\int 1 + (cos (x))^{2} d x

integral from 0 to 2 of 3/(4x^2+5x+1)

\int_{0}^{2} \frac{3}{4 x ^{2} + 5 x + 1} d x

(\partial)/(\partial x)({f}(x))

\frac{\partial}{\partial x} (f (x))

integral of 1/((x-1)^3)

\int \frac{1}{( x - 1 ) ^{3}} d x

Frequently Asked Questions (FAQ)

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