What is ((cos(2x))^{x^3})^{-5^'} ?

The solution to ((cos(2x))^{x^3})^{-5^'} is cos^{-5^'x^3}(2x)

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simplify ((cos(2x))^{x^3})^{-5^'}

simplify

((cos (2 x))^{x^{3}})^{- 5^{^{'}}}

cos^{- 5^{'} x^{3}} (2 x)

Solution steps

((cos (2 x))^{x^{3}})^{- 5^{^{'}}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

= (cos (2 x))^{x^{3} (- 5^{^{^{'}}})}

Remove parentheses:

(- a) = - a

= (cos (2 x))^{- 5^{^{^{'}}} x^{3}}

Remove parentheses:

(a) = a

= cos^{- 5^{^{^{'}}} x^{3}} (2 x)

e \cdot (- 2) e^{- 2 x}

3 e^{2 t} \cdot 6 e^{2 t}

e^{- x} \cdot 3 e^{- x}

8^{\frac{3}{4}} \cdot 3^{\frac{3}{4}}

(2 x^{5}) \cdot (3 x^{2})

What is ((cos(2x))^{x^3})^{-5^'} ?
The solution to ((cos(2x))^{x^3})^{-5^'} is cos^{-5^'x^3}(2x)