What is the derivative of 5^{ln(cos(3x)}) ?

The derivative of 5^{ln(cos(3x)}) is -3ln(5)tan(3x)cos^{ln(5)}(3x)

What is the first derivative of 5^{ln(cos(3x)}) ?

The first derivative of 5^{ln(cos(3x)}) is -3ln(5)tan(3x)cos^{ln(5)}(3x)

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\frac{d}{d x} (5^{l n (c o s (3 x))})

- 3 ln (5) tan (3 x) cos^{l n (5)} (3 x)

Solution steps

\frac{d}{d x} (5^{l n (c o s (3 x))})

Apply exponent rule:

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

5^{l n (c o s (3 x))} = e^{l n (c o s (3 x)) l n (5)}

= \frac{d}{d x} (e^{l n (c o s (3 x)) l n (5)})

Apply the chain rule:

e^{l n (c o s (3 x)) l n (5)} \frac{d}{d x} (ln (cos (3 x)) ln (5))

= e^{l n (c o s (3 x)) l n (5)} \frac{d}{d x} (ln (cos (3 x)) ln (5))

\frac{d}{d x} (ln (cos (3 x)) ln (5)) = - 3 ln (5) tan (3 x)

= e^{l n (c o s (3 x)) l n (5)} (- 3 ln (5) tan (3 x))

Simplify

e^{l n (c o s (3 x)) l n (5)} (- 3 ln (5) tan (3 x)) : - 3 ln (5) tan (3 x) cos^{l n (5)} (3 x)

= - 3 ln (5) tan (3 x) cos^{l n (5)} (3 x)

\frac{d}{d x} (- 3 x + 2)

\int - 2 x^{2} + 4 x d x

\frac{\partial}{\partial x} (9 x y + sin (y))

\frac{\partial}{\partial x} (\frac{5 x + 8}{4 y + 1})

f (x) = (4 x)

What is the derivative of 5^{ln(cos(3x)}) ?
The derivative of 5^{ln(cos(3x)}) is -3ln(5)tan(3x)cos^{ln(5)}(3x)
What is the first derivative of 5^{ln(cos(3x)}) ?
The first derivative of 5^{ln(cos(3x)}) is -3ln(5)tan(3x)cos^{ln(5)}(3x)