What is the d/(dt)((x)(sin^2(t))) ?

The d/(dt)((x)(sin^2(t))) is (dx)/(dt)sin^2(t)+sin(2t)x

What is the first d/(dt)((x)(sin^2(t))) ?

The first d/(dt)((x)(sin^2(t))) is (dx)/(dt)sin^2(t)+sin(2t)x

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\frac{4 - x ^{2}}{x - 2}

(cos (sin (x)))^{3}

e^{8} - 1

5 a^{2} z - 12 x c - 4 a^{2} c + 15 x z

What is the d/(dt)((x)(sin^2(t))) ?
The d/(dt)((x)(sin^2(t))) is (dx)/(dt)sin^2(t)+sin(2t)x
What is the first d/(dt)((x)(sin^2(t))) ?
The first d/(dt)((x)(sin^2(t))) is (dx)/(dt)sin^2(t)+sin(2t)x