What is the derivative of tan(sqrt(cos^2(x^5))) ?

The derivative of tan(sqrt(cos^2(x^5))) is -5x^4sec^2(cos(x^5))sin(x^5)

What is the first derivative of tan(sqrt(cos^2(x^5))) ?

The first derivative of tan(sqrt(cos^2(x^5))) is -5x^4sec^2(cos(x^5))sin(x^5)

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\frac{d}{d x} (tan (cos^{2} (x^{5})))

- 5 x^{4} sec^{2} (cos (x^{5})) sin (x^{5})

Solution steps

\frac{d}{d x} (tan (cos^{2} (x^{5})))

Apply the chain rule:

sec^{2} (cos^{2} (x^{5})) \frac{d}{d x} (cos^{2} (x^{5}))

= sec^{2} (cos^{2} (x^{5})) \frac{d}{d x} (cos^{2} (x^{5}))

\frac{d}{d x} (cos^{2} (x^{5})) = - \frac{5 x ^{4} cos ( x ^{5} ) sin ( x ^{5} )}{cos ^{2} ( x ^{5} )}

= sec^{2} (cos^{2} (x^{5})) (- \frac{5 x ^{4} cos ( x ^{5} ) sin ( x ^{5} )}{cos ^{2} ( x ^{5} )})

Simplify

sec^{2} (cos^{2} (x^{5})) (- \frac{5 x ^{4} cos ( x ^{5} ) sin ( x ^{5} )}{cos ^{2} ( x ^{5} )}) : - 5 x^{4} sec^{2} (cos (x^{5})) sin (x^{5})

= - 5 x^{4} sec^{2} (cos (x^{5})) sin (x^{5})

x \to 0 lim (\frac{7 x ^{2} - 4 x}{x})

\frac{d}{d t} (a sin (t))

e^{2} t cos (2 t)

\int \frac{6}{7} x^{- \frac{1}{7}} d x

x \to 3 - lim ((x - 3)^{- 1})

What is the derivative of tan(sqrt(cos^2(x^5))) ?
The derivative of tan(sqrt(cos^2(x^5))) is -5x^4sec^2(cos(x^5))sin(x^5)
What is the first derivative of tan(sqrt(cos^2(x^5))) ?
The first derivative of tan(sqrt(cos^2(x^5))) is -5x^4sec^2(cos(x^5))sin(x^5)