What is the derivative of (y^2(5sin(x)+5cos(x))) ?

The derivative of (y^2(5sin(x)+5cos(x))) is 2y(dy)/(dx)(5sin(x)+5cos(x))+(5cos(x)-5sin(x))y^2

What is the first derivative of (y^2(5sin(x)+5cos(x))) ?

The first derivative of (y^2(5sin(x)+5cos(x))) is 2y(dy)/(dx)(5sin(x)+5cos(x))+(5cos(x)-5sin(x))y^2

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\frac{d}{d x} ((y^{2}) (5 sin (x) + 5 cos (x)))

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

Solution steps

\frac{d}{d x} ((y^{2}) (5 sin (x) + 5 cos (x)))

Apply the Product Rule:

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

f = y^{2}, g = 5 sin (x) + 5 cos (x)

= \frac{d}{d x} (y^{2}) (5 sin (x) + 5 cos (x)) + \frac{d}{d x} (5 sin (x) + 5 cos (x)) y^{2}

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

\frac{d}{d x} (5 sin (x) + 5 cos (x)) = 5 cos (x) - 5 sin (x)

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

(s^{2} + 4) \cdot (s^{2} + \frac{4}{3})

(- 3 x + 2 + 1)^{2}

\frac{( - y + 4 ) ^{3}}{24}

(\frac{5}{3 x} + \frac{5}{x} = 1) 3 x

(- \frac{5}{2} - x) (- 3 - x) - 3

What is the derivative of (y^2(5sin(x)+5cos(x))) ?
The derivative of (y^2(5sin(x)+5cos(x))) is 2y(dy)/(dx)(5sin(x)+5cos(x))+(5cos(x)-5sin(x))y^2
What is the first derivative of (y^2(5sin(x)+5cos(x))) ?
The first derivative of (y^2(5sin(x)+5cos(x))) is 2y(dy)/(dx)(5sin(x)+5cos(x))+(5cos(x)-5sin(x))y^2