What is the derivative of 3^{cos(2x}) ?

The derivative of 3^{cos(2x}) is -2ln(3)*3^{cos(2x)}sin(2x)

What is the first derivative of 3^{cos(2x}) ?

The first derivative of 3^{cos(2x}) is -2ln(3)*3^{cos(2x)}sin(2x)

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\frac{d}{d x} (3^{c o s (2 x)})

- 2 ln (3) \cdot 3^{c o s (2 x)} sin (2 x)

Solution steps

\frac{d}{d x} (3^{c o s (2 x)})

Apply exponent rule:

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

3^{c o s (2 x)} = e^{c o s (2 x) l n (3)}

= \frac{d}{d x} (e^{c o s (2 x) l n (3)})

Apply the chain rule:

e^{c o s (2 x) l n (3)} \frac{d}{d x} (cos (2 x) ln (3))

= e^{c o s (2 x) l n (3)} \frac{d}{d x} (cos (2 x) ln (3))

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

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

Simplify

e^{c o s (2 x) l n (3)} (- 2 ln (3) sin (2 x)) : - 2 ln (3) \cdot 3^{c o s (2 x)} sin (2 x)

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

x \to 3 lim (\frac{10}{x ^{2}})

\int_{0}^{4} (\frac{5 x}{x ^{2} + 9}) d x

\int (x + 6) (x - 7) d x

\frac{\partial}{\partial x} (\frac{x + q}{x + r})

\frac{d}{d x} ((2 x + x) (x^{2} - x))

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