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

The derivative of (sin^2(x)dx) is d(xsin(2x)+sin^2(x))

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

The first derivative of (sin^2(x)dx) is d(xsin(2x)+sin^2(x))

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

d (x sin (2 x) + sin^{2} (x))

Solution steps

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

Treat

d

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

= d (sin (2 x) x + 1 \cdot sin^{2} (x))

Simplify

= d (x sin (2 x) + sin^{2} (x))

\int \frac{x ^{2} + 5 x ^{3} - 7}{x ^{2}} d x

\int \frac{9 x}{1 + x ^{4}} d x

x \to 2 - lim (x + 5)

\frac{5 x}{x + 3}

\int 2 + x d x

What is the derivative of (sin^2(x)dx) ?
The derivative of (sin^2(x)dx) is d(xsin(2x)+sin^2(x))
What is the first derivative of (sin^2(x)dx) ?
The first derivative of (sin^2(x)dx) is d(xsin(2x)+sin^2(x))