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Popular >

derivative of 6ycos(x)

Solution

\frac{d}{d x} (6 y cos (x))

Solution

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

Solution steps

\frac{d}{d x} (6 y cos (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (y cos (x))

Apply the Product Rule:

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

f = y, g = cos (x)

= 6 (\frac{d y}{d x} cos (x) + \frac{d}{d x} (cos (x)) y)

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

= 6 (\frac{d y}{d x} cos (x) + (- sin (x)) y)

Simplify

= 6 (cos (x) \frac{d y}{d x} - sin (x) y)

Popular Examples

limit as x approaches 81 of log_{243}(x)

x \to 81 lim (lo g_{243} (x))

limit as x approaches infinity of x^4-1

x \to \infty lim (x^{4} - 1)

(\partial)/(\partial x)(x^y-y^x)

\frac{\partial}{\partial x} (x^{y} - y^{x})

tangent of 4x^2,\at x=3 tangent of

4 x^{2}, at x = 3

(\partial)/(\partial θ)(θ)

\frac{\partial}{\partial θ} (θ)

Frequently Asked Questions (FAQ)

What is the derivative of 6ycos(x) ?
The derivative of 6ycos(x) is 6(cos(x)(dy)/(dx)-sin(x)y)
What is the first derivative of 6ycos(x) ?
The first derivative of 6ycos(x) is 6(cos(x)(dy)/(dx)-sin(x)y)