What is the derivative of-3^{-2}(tan(7t))^5 ?

The derivative of-3^{-2}(tan(7t))^5 is -35/9 tan^4(7t)sec^2(7t)

What is the first derivative of-3^{-2}(tan(7t))^5 ?

The first derivative of-3^{-2}(tan(7t))^5 is -35/9 tan^4(7t)sec^2(7t)

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derivative of

- 3^{- 2} (tan (7 t))^{5}

- \frac{35}{9} tan^{4} (7 t) sec^{2} (7 t)

Solution steps

\frac{d}{d t} (- 3^{- 2} (tan (7 t))^{5})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 3^{- 2} \frac{d}{d t} ((tan (7 t))^{5})

Apply the chain rule:

5 (tan (7 t))^{4} \frac{d}{d t} (tan (7 t))

= 5 (tan (7 t))^{4} \frac{d}{d t} (tan (7 t))

\frac{d}{d t} (tan (7 t)) = sec^{2} (7 t) \cdot 7

= - 3^{- 2} \cdot 5 (tan (7 t))^{4} sec^{2} (7 t) \cdot 7

Simplify

- 3^{- 2} \cdot 5 tan^{4} (7 t) sec^{2} (7 t) \cdot 7 : - \frac{35}{9} tan^{4} (7 t) sec^{2} (7 t)

= - \frac{35}{9} tan^{4} (7 t) sec^{2} (7 t)

x \to 3 lim (\frac{\frac{x}{3} + 2}{x + 1})

\frac{d}{d x} (\frac{x ^{3}}{x ^{2} - 4})

\frac{d}{d x} (\frac{1 + csc ( x ^{6} )}{1 - cot ( x ^{6} )})

y = x^{2} - 7 x + 6, x = 2, x = 6

ln (121 sin^{2} (x))

What is the derivative of-3^{-2}(tan(7t))^5 ?
The derivative of-3^{-2}(tan(7t))^5 is -35/9 tan^4(7t)sec^2(7t)
What is the first derivative of-3^{-2}(tan(7t))^5 ?
The first derivative of-3^{-2}(tan(7t))^5 is -35/9 tan^4(7t)sec^2(7t)