What is the d/(dt)((x)(3xt^2)) ?

The d/(dt)((x)(3xt^2)) is 3(2tx^2+2x(dx)/(dt)t^2)

What is the first d/(dt)((x)(3xt^2)) ?

The first d/(dt)((x)(3xt^2)) is 3(2tx^2+2x(dx)/(dt)t^2)

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\frac{d}{d t} ((x) (3 x t^{2}))

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

Solution steps

\frac{d}{d t} ((x) (3 x t^{2}))

Simplify

(x) (3 x t^{2}) : 3 t^{2} x^{2}

= \frac{d}{d t} (3 t^{2} x^{2})

Take the constant out:

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

= 3 \frac{d}{d t} (t^{2} x^{2})

Apply the Product Rule:

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

f = t^{2}, g = x^{2}

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

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

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

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

\frac{d}{d t} ((x) (1 7^{t}))

4 x - 20 x + 9

m^{2} e^{m x} - 5 m e^{m x} + 6 e^{m x}

2 x^{3} - 3 x^{3}

x 32 x 2 - x - 2

What is the d/(dt)((x)(3xt^2)) ?
The d/(dt)((x)(3xt^2)) is 3(2tx^2+2x(dx)/(dt)t^2)
What is the first d/(dt)((x)(3xt^2)) ?
The first d/(dt)((x)(3xt^2)) is 3(2tx^2+2x(dx)/(dt)t^2)