What is the derivative of x^3y^5-2x^2y+x ?

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

What is the first derivative of x^3y^5-2x^2y+x ?

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

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\frac{d}{d x} (x^{3} y^{5} - 2 x^{2} y + x)

3 x^{2} y^{5} + 5 y^{4} \frac{d y}{d x} x^{3} - 2 (2 x y + \frac{d y}{d x} x^{2}) + 1

Solution steps

\frac{d}{d x} (x^{3} y^{5} - 2 x^{2} y + x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{3} y^{5}) - \frac{d}{d x} (2 x^{2} y) + \frac{d x}{d x}

\frac{d}{d x} (x^{3} y^{5}) = 3 x^{2} y^{5} + 5 y^{4} \frac{d y}{d x} x^{3}

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

\frac{d x}{d x} = 1

= 3 x^{2} y^{5} + 5 y^{4} \frac{d y}{d x} x^{3} - 2 (2 x y + \frac{d y}{d x} x^{2}) + 1

\int (x - 2) (x + 2) d x

f (x) = 4 tan (x), at x = \frac{π}{6}

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

\frac{d}{d x} (cos (x) sin^{2} (x))

y^{^{'}} = - 4 x y

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