en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

d/(dt)((x)(a(t+sin(t)cos(t))))

Solution

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

Solution

x a (1 + cos^{2} (t) - sin^{2} (t))

Solution steps

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

Treat

a, x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d t}{d t} = 1

\frac{d}{d t} (sin (t) cos (t)) = cos^{2} (t) - sin^{2} (t)

= x a (1 + cos^{2} (t) - sin^{2} (t))

Popular Examples

expand log_{a}(b)log_{b}(c)log_{c}(a)expand

lo g_{a} (b) lo g_{b} (c) lo g_{c} (a)

simplify 1+(0.024X)/((s+0.2)(s+0.1))simplify

1 + \frac{0.024 X}{( s + 0.2 ) ( s + 0.1 )}

expand argument(1+i)expand

a r gu m e n t (1 + i)

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

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

expand 2x^{(10x-1)(10x+1)}expand

2 x^{(10 x - 1) (10 x + 1)}

Frequently Asked Questions (FAQ)

What is the d/(dt)((x)(a(t+sin(t)cos(t)))) ?
The d/(dt)((x)(a(t+sin(t)cos(t)))) is xa(1+cos^2(t)-sin^2(t))
What is the first d/(dt)((x)(a(t+sin(t)cos(t)))) ?
The first d/(dt)((x)(a(t+sin(t)cos(t)))) is xa(1+cos^2(t)-sin^2(t))