What is the derivative of 4^{cos(3t)} ?

The derivative of 4^{cos(3t)} is -3ln(2)*2^{2cos(3t)+1}sin(3t)

What is the first derivative of 4^{cos(3t)} ?

The first derivative of 4^{cos(3t)} is -3ln(2)*2^{2cos(3t)+1}sin(3t)

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derivative of

4^{c o s (3 t)}

- 3 ln (2) \cdot 2^{2 c o s (3 t) + 1} sin (3 t)

Solution steps

\frac{d}{d t} (4^{c o s (3 t)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

4^{c o s (3 t)} = e^{c o s (3 t) l n (4)}

= \frac{d}{d t} (e^{c o s (3 t) l n (4)})

Apply the chain rule:

e^{c o s (3 t) l n (4)} \frac{d}{d t} (cos (3 t) ln (4))

= e^{c o s (3 t) l n (4)} \frac{d}{d t} (cos (3 t) ln (4))

\frac{d}{d t} (cos (3 t) ln (4)) = - 6 ln (2) sin (3 t)

= e^{c o s (3 t) l n (4)} (- 6 ln (2) sin (3 t))

Simplify

e^{c o s (3 t) l n (4)} (- 6 ln (2) sin (3 t)) : - 3 ln (2) \cdot 2^{2 c o s (3 t) + 1} sin (3 t)

= - 3 ln (2) \cdot 2^{2 c o s (3 t) + 1} sin (3 t)

sin (t - π)

\int \frac{3 x}{x ^{2} - x - 2} d x

(x - 1) d y + (y - x^{2} + 2 x^{- 3}) d x = 0

x = y^{\frac{1}{2}}, x = 2 [0, 2]

f (x) = x^{2}, at x = 0.2

What is the derivative of 4^{cos(3t)} ?
The derivative of 4^{cos(3t)} is -3ln(2)*2^{2cos(3t)+1}sin(3t)
What is the first derivative of 4^{cos(3t)} ?
The first derivative of 4^{cos(3t)} is -3ln(2)*2^{2cos(3t)+1}sin(3t)