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Popular >

d/(dt)((x)(t+sin(t)-1))

Solution

\frac{d}{d t} ((x) (t + sin (t) - 1))

Solution

\frac{d x}{d t} (t + sin (t) - 1) + (cos (t) + 1) x

Solution steps

\frac{d}{d t} ((x) (t + sin (t) - 1))

Apply the Product Rule:

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

f = x, g = t + sin (t) - 1

= \frac{d x}{d t} (t + sin (t) - 1) + \frac{d}{d t} (t + sin (t) - 1) x

\frac{d}{d t} (t + sin (t) - 1) = cos (t) + 1

= \frac{d x}{d t} (t + sin (t) - 1) + (cos (t) + 1) x

Popular Examples

expand (4(s+2))/((s+1)(s+3))expand

\frac{4 ( s + 2 )}{( s + 1 ) ( s + 3 )}

expand (ae^3-2a^2+4)(ae^3-3a)expand

(a e^{3} - 2 a^{2} + 4) (a e^{3} - 3 a)

expand 2/((4+h)^2)expand

\frac{2}{( 4 + h ) ^{2}}

expand (a-2,b-2)(b/a)^3 expand

(a - 2, b - 2) (\frac{b}{a})^{3}

expand 3*10.2 expand

3 \cdot 10.2

Frequently Asked Questions (FAQ)

What is the d/(dt)((x)(t+sin(t)-1)) ?
The d/(dt)((x)(t+sin(t)-1)) is (dx)/(dt)(t+sin(t)-1)+(cos(t)+1)x
What is the first d/(dt)((x)(t+sin(t)-1)) ?
The first d/(dt)((x)(t+sin(t)-1)) is (dx)/(dt)(t+sin(t)-1)+(cos(t)+1)x