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Popular >

derivative of ky(x^2)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

Popular Examples

y^{^{''}} - y = 3 e^{x}

derivative of (1/(x^2+3)(x^2-1/(x^2)+3))

\frac{d}{d x} ((\frac{1}{x ^{2}} + 3) (x^{2} - \frac{1}{x ^{2}} + 3))

limit as n approaches infinity of ((-1)^{n+1})/(2n-1)

n \to \infty lim (\frac{( - 1 ) ^{n + 1}}{2 n - 1})

integral from 0 to pi/2 of sin^5(xco)s^{12}x

\int_{0}^{\frac{π}{2}} sin^{5} (x co) s^{12} x

(\partial)/(\partial x)(x^{1/2}*y^{1/2})

\frac{\partial}{\partial x} (x^{\frac{1}{2}} \cdot y^{\frac{1}{2}})

Frequently Asked Questions (FAQ)

What is the derivative of ky(x^2) ?
The derivative of ky(x^2) is k(derivative of {y}(x)x^2+2x{y}(x))
What is the first derivative of ky(x^2) ?
The first derivative of ky(x^2) is k(derivative of {y}(x)x^2+2x{y}(x))