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Popular >

derivative of (1-x^2+10(y-x^2)^2)

Solution

\frac{d}{d x} ((1 - x)^{2} + 10 (y - x^{2})^{2})

Solution

- 2 (1 - x) + 20 (y - x^{2}) (\frac{d y}{d x} - 2 x)

Solution steps

\frac{d}{d x} ((1 - x)^{2} + 10 (y - x^{2})^{2})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} ((1 - x)^{2}) + \frac{d}{d x} (10 (y - x^{2})^{2})

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

\frac{d}{d x} (10 (y - x^{2})^{2}) = 20 (y - x^{2}) (\frac{d y}{d x} - 2 x)

= - 2 (1 - x) + 20 (y - x^{2}) (\frac{d y}{d x} - 2 x)

Popular Examples

derivative of sqrt(3x-sin^2(4x))

\frac{d}{d x} (3 x - sin^{2} (4 x))

limit as x approaches 0 of x/(e^{7x)-1}

x \to 0 lim (\frac{x}{e ^{7 x} - 1})

y^{^{'}} + 4 y = 32

limit as x approaches 3 of 3

x \to 3 lim (3)

inverse oflaplace (e^{-s})/(s^2+s)inverse laplace

\frac{e ^{- s}}{s ^{2} + s}

Frequently Asked Questions (FAQ)

What is the derivative of (1-x^2+10(y-x^2)^2) ?
The derivative of (1-x^2+10(y-x^2)^2) is -2(1-x)+20(y-x^2)((dy)/(dx)-2x)
What is the first derivative of (1-x^2+10(y-x^2)^2) ?
The first derivative of (1-x^2+10(y-x^2)^2) is -2(1-x)+20(y-x^2)((dy)/(dx)-2x)