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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (sin (y)) = cos (y) \frac{d y}{d x}

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

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

x \to 5 lim (h (x))

y^{^{'}} + 5 (tan (5 x)) y = - 8 (cos (5 x))

1 - cos (7 t)

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

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

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