What is the derivative of x^4+4x^2(y-2+5(y-1)^2) ?

The derivative of x^4+4x^2(y-2+5(y-1)^2) is 4x^3+4(2x(y-2)+(dy)/(dx)x^2)+10(y-1)(dy)/(dx)

What is the first derivative of x^4+4x^2(y-2+5(y-1)^2) ?

The first derivative of x^4+4x^2(y-2+5(y-1)^2) is 4x^3+4(2x(y-2)+(dy)/(dx)x^2)+10(y-1)(dy)/(dx)

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\frac{d}{d x} (x^{4} + 4 x^{2} (y - 2) + 5 (y - 1)^{2})

4 x^{3} + 4 (2 x (y - 2) + \frac{d y}{d x} x^{2}) + 10 (y - 1) \frac{d y}{d x}

Solution steps

\frac{d}{d x} (x^{4} + 4 x^{2} (y - 2) + 5 (y - 1)^{2})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{4}) + \frac{d}{d x} (4 x^{2} (y - 2)) + \frac{d}{d x} (5 (y - 1)^{2})

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (4 x^{2} (y - 2)) = 4 (2 x (y - 2) + \frac{d y}{d x} x^{2})

\frac{d}{d x} (5 (y - 1)^{2}) = 10 (y - 1) \frac{d y}{d x}

= 4 x^{3} + 4 (2 x (y - 2) + \frac{d y}{d x} x^{2}) + 10 (y - 1) \frac{d y}{d x}

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

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

f (x) = \frac{2 x + 8 x ^{2}}{( 1 + 8 x ) ^{2}}

n = 0 \sum \infty \frac{1}{n ^{1}}

y^{^{''}} + 8 y^{^{'}} + 15 y = 4

What is the derivative of x^4+4x^2(y-2+5(y-1)^2) ?
The derivative of x^4+4x^2(y-2+5(y-1)^2) is 4x^3+4(2x(y-2)+(dy)/(dx)x^2)+10(y-1)(dy)/(dx)
What is the first derivative of x^4+4x^2(y-2+5(y-1)^2) ?
The first derivative of x^4+4x^2(y-2+5(y-1)^2) is 4x^3+4(2x(y-2)+(dy)/(dx)x^2)+10(y-1)(dy)/(dx)