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

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

\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

\frac{( x ^{n + 1} - ( n + 1 ) x + n )}{x - 1}

6 sin (30 (t + 2))

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

(4 + 2 ln (2))^{2}

(3 x y^{2} + 3 x^{2}) d x + (2 x^{2} y + 4 y^{3}) d x

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