What is the derivative of ta{g}(t,xx) ?

The derivative of ta{g}(t,xx) is ta(derivative of {g}(t,x)x+1*{g}(t,x))

What is the first derivative of ta{g}(t,xx) ?

The first derivative of ta{g}(t,xx) is ta(derivative of {g}(t,x)x+1*{g}(t,x))

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\frac{d}{d x} (t a g (t, x) x)

t a (\frac{d}{d x} (g (t, x)) x + 1 \cdot g (t, x))

Solution steps

\frac{d}{d x} (t a g (t, x) x)

Treat

a, t

as a constant

Take the constant out:

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

= t a \frac{d}{d x} (g (t, x) x)

Apply the Product Rule:

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

f = g (t, x), g = x

= t a (\frac{d}{d x} (g (t, x)) x + \frac{d x}{d x} g (t, x))

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

= t a (\frac{d}{d x} (g (t, x)) x + 1 \cdot g (t, x))

What is the derivative of ta{g}(t,xx) ?
The derivative of ta{g}(t,xx) is ta(derivative of {g}(t,x)x+1*{g}(t,x))
What is the first derivative of ta{g}(t,xx) ?
The first derivative of ta{g}(t,xx) is ta(derivative of {g}(t,x)x+1*{g}(t,x))