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Popular Calculus >

d/(dt)(20sin(2t-3x))

Solution

\frac{d}{d t} (20 sin (2 t - 3 x))

Solution

20 cos (2 t - 3 x) (2 - 3 \frac{d x}{d t})

Solution steps

\frac{d}{d t} (20 sin (2 t - 3 x))

Take the constant out:

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

= 20 \frac{d}{d t} (sin (2 t - 3 x))

Apply the chain rule:

cos (2 t - 3 x) \frac{d}{d t} (2 t - 3 x)

= cos (2 t - 3 x) \frac{d}{d t} (2 t - 3 x)

\frac{d}{d t} (2 t - 3 x) = 2 - 3 \frac{d x}{d t}

= 20 cos (2 t - 3 x) (2 - 3 \frac{d x}{d t})

Popular Examples

derivative of y=3x^7

d er i v a t i v e y = 3 x^{7}

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d er i v a t i v e 2 y^{2} + 1

d/(dt)(a(cos(t)+log_{10}((tan(t))/2)))

\frac{d}{d t} (a (cos (t) + lo g_{10} (\frac{tan ( t )}{2})))

derivative of sqrt(((1+x))/((1+x^2)))

d er i v a t i v e \frac{( 1 + x )}{( 1 + x ^{2} )}

derivative of (x+1)/(2x-1)

d er i v a t i v e \frac{x + 1}{2 x - 1}

Frequently Asked Questions (FAQ)

What is the d/(dt)(20sin(2t-3x)) ?
The d/(dt)(20sin(2t-3x)) is 20cos(2t-3x)(2-3(dx)/(dt))
What is the first d/(dt)(20sin(2t-3x)) ?
The first d/(dt)(20sin(2t-3x)) is 20cos(2t-3x)(2-3(dx)/(dt))