What is the derivative of 2^{cot(5x}) ?

The derivative of 2^{cot(5x}) is -5ln(2)*2^{cot(5x)}csc^2(5x)

What is the first derivative of 2^{cot(5x}) ?

The first derivative of 2^{cot(5x}) is -5ln(2)*2^{cot(5x)}csc^2(5x)

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\frac{d}{d x} (2^{c o t (5 x)})

- 5 ln (2) \cdot 2^{c o t (5 x)} csc^{2} (5 x)

Solution steps

\frac{d}{d x} (2^{c o t (5 x)})

Apply exponent rule:

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

2^{c o t (5 x)} = e^{c o t (5 x) l n (2)}

= \frac{d}{d x} (e^{c o t (5 x) l n (2)})

Apply the chain rule:

e^{c o t (5 x) l n (2)} \frac{d}{d x} (cot (5 x) ln (2))

= e^{c o t (5 x) l n (2)} \frac{d}{d x} (cot (5 x) ln (2))

\frac{d}{d x} (cot (5 x) ln (2)) = - 5 ln (2) csc^{2} (5 x)

= e^{c o t (5 x) l n (2)} (- 5 ln (2) csc^{2} (5 x))

Simplify

e^{c o t (5 x) l n (2)} (- 5 ln (2) csc^{2} (5 x)) : - 5 ln (2) \cdot 2^{c o t (5 x)} csc^{2} (5 x)

= - 5 ln (2) \cdot 2^{c o t (5 x)} csc^{2} (5 x)

\frac{d}{d x} (\frac{1}{x ( ln ( x ) ) ^{2}})

\int \frac{( x - 2 ) 1 - x ^{2} + x}{1 - x ^{2}} d x

\int x sec^{2} (5 x) d x

y^{^{''}} + 4 y = - 2

\int cos (φ) d φ

What is the derivative of 2^{cot(5x}) ?
The derivative of 2^{cot(5x}) is -5ln(2)*2^{cot(5x)}csc^2(5x)
What is the first derivative of 2^{cot(5x}) ?
The first derivative of 2^{cot(5x}) is -5ln(2)*2^{cot(5x)}csc^2(5x)