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Popular >

d/(dt)(e^{5tsin(2t)})

Solution

\frac{d}{d t} (e^{5 t s i n (2 t)})

Solution

e^{5 t s i n (2 t)} \cdot 5 (sin (2 t) + 2 t cos (2 t))

Solution steps

\frac{d}{d t} (e^{5 t s i n (2 t)})

Apply the chain rule:

e^{5 t s i n (2 t)} \frac{d}{d t} (5 t sin (2 t))

= e^{5 t s i n (2 t)} \frac{d}{d t} (5 t sin (2 t))

\frac{d}{d t} (5 t sin (2 t)) = 5 (sin (2 t) + 2 t cos (2 t))

= e^{5 t s i n (2 t)} \cdot 5 (sin (2 t) + 2 t cos (2 t))

Popular Examples

derivative of e^{ln(x})

\frac{d}{d x} (e^{l n (x)})

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

\frac{x ^{2} - 1}{x ^{2} + 1}

sum from n=2 to infinity of ln(1/n)

n = 2 \sum \infty ln (\frac{1}{n})

inverse oflaplace 1/(2x^2+x+1)inverse laplace

\frac{1}{2 x ^{2} + x + 1}

(dN)/(dt)=5-N,N(2)=2

\frac{d N}{d t} = 5 - N, N (2) = 2

Frequently Asked Questions (FAQ)

What is the d/(dt)(e^{5tsin(2t)}) ?
The d/(dt)(e^{5tsin(2t)}) is e^{5tsin(2t)}*5(sin(2t)+2tcos(2t))
What is the first d/(dt)(e^{5tsin(2t)}) ?
The first d/(dt)(e^{5tsin(2t)}) is e^{5tsin(2t)}*5(sin(2t)+2tcos(2t))