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Popular >

derivative of (1+2xsqrt(y))

Solution

\frac{d}{d x} ((1 + 2 x) y)

Solution

2 y + \frac{\frac{d y}{d x} ( 1 + 2 x )}{2 y}

Solution steps

\frac{d}{d x} ((1 + 2 x) y)

Apply the Product Rule:

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

f = 1 + 2 x, g = y

= \frac{d}{d x} (1 + 2 x) y + \frac{d}{d x} (y) (1 + 2 x)

\frac{d}{d x} (1 + 2 x) = 2

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

= 2 y + \frac{\frac{d y}{d x}}{2 y} (1 + 2 x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 2 y + \frac{\frac{d y}{d x} ( 1 + 2 x )}{2 y}

Popular Examples

integral from 4 to 9 of 1/2 y^{1/2}+1/2 y^{-1/2}

\int_{4}^{9} \frac{1}{2} y^{\frac{1}{2}} + \frac{1}{2} y^{- \frac{1}{2}} d y

derivative of a(2e^{-2x}x-2e^{-2x}x^2)

\frac{d}{d x} (a (2 e^{- 2 x} x - 2 e^{- 2 x} x^{2}))

integral from-2 to 4 of x+2

\int_{- 2}^{4} x + 2 d x

(\partial)/(\partial y)(-y/(y^2+x^2))

\frac{\partial}{\partial y} (- \frac{y}{y ^{2} + x ^{2}})

y^{''}+5y^'+4y=2te^{3t}

y^{^{''}} + 5 y^{^{'}} + 4 y = 2 t e^{3 t}

Frequently Asked Questions (FAQ)

What is the derivative of (1+2xsqrt(y)) ?
The derivative of (1+2xsqrt(y)) is 2sqrt(y)+(\frac{dy)/(dx)(1+2x)}{2sqrt(y)}
What is the first derivative of (1+2xsqrt(y)) ?
The first derivative of (1+2xsqrt(y)) is 2sqrt(y)+(\frac{dy)/(dx)(1+2x)}{2sqrt(y)}