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Popular >

d/(dt)((x)((t^2+5t)(t-10)))

Solution

\frac{d}{d t} ((x) ((t^{2} + 5 t) (t - 10)))

Solution

\frac{d x}{d t} (t^{2} + 5 t) (t - 10) + (3 t^{2} - 10 t - 50) x

Solution steps

\frac{d}{d t} ((x) ((t^{2} + 5 t) (t - 10)))

Apply the Product Rule:

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

f = x, g = (t^{2} + 5 t) (t - 10)

= \frac{d x}{d t} (t^{2} + 5 t) (t - 10) + \frac{d}{d t} ((t^{2} + 5 t) (t - 10)) x

\frac{d}{d t} ((t^{2} + 5 t) (t - 10)) = 3 t^{2} - 10 t - 50

= \frac{d x}{d t} (t^{2} + 5 t) (t - 10) + (3 t^{2} - 10 t - 50) x

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\frac{7 ( 38 - 2 b )}{5}

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f (- 2, - 3)

Frequently Asked Questions (FAQ)

What is the d/(dt)((x)((t^2+5t)(t-10))) ?
The d/(dt)((x)((t^2+5t)(t-10))) is (dx)/(dt)(t^2+5t)(t-10)+(3t^2-10t-50)x
What is the first d/(dt)((x)((t^2+5t)(t-10))) ?
The first d/(dt)((x)((t^2+5t)(t-10))) is (dx)/(dt)(t^2+5t)(t-10)+(3t^2-10t-50)x