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Popular >

d/(dt)((x)(2sinh(t)+3t^2))

Solution

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

Solution

\frac{d x}{d t} (2 sinh (t) + 3 t^{2}) + (2 cosh (t) + 6 t) x

Solution steps

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

Apply the Product Rule:

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

f = x, g = 2 sinh (t) + 3 t^{2}

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

\frac{d}{d t} (2 sinh (t) + 3 t^{2}) = 2 cosh (t) + 6 t

= \frac{d x}{d t} (2 sinh (t) + 3 t^{2}) + (2 cosh (t) + 6 t) x

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Frequently Asked Questions (FAQ)

What is the d/(dt)((x)(2sinh(t)+3t^2)) ?
The d/(dt)((x)(2sinh(t)+3t^2)) is (dx)/(dt)(2sinh(t)+3t^2)+(2cosh(t)+6t)x
What is the first d/(dt)((x)(2sinh(t)+3t^2)) ?
The first d/(dt)((x)(2sinh(t)+3t^2)) is (dx)/(dt)(2sinh(t)+3t^2)+(2cosh(t)+6t)x