What is the derivative of cos(xsec^7(x)) ?

The derivative of cos(xsec^7(x)) is 6sec^7(x)sin(x)

What is the first derivative of cos(xsec^7(x)) ?

The first derivative of cos(xsec^7(x)) is 6sec^7(x)sin(x)

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\frac{d}{d x} (cos (x) sec^{7} (x))

6 sec^{7} (x) sin (x)

Solution steps

\frac{d}{d x} (cos (x) sec^{7} (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (x), g = sec^{7} (x)

= \frac{d}{d x} (cos (x)) sec^{7} (x) + \frac{d}{d x} (sec^{7} (x)) cos (x)

\frac{d}{d x} (cos (x)) = - sin (x)

\frac{d}{d x} (sec^{7} (x)) = 7 sec^{7} (x) tan (x)

= (- sin (x)) sec^{7} (x) + 7 sec^{7} (x) tan (x) cos (x)

Simplify

(- sin (x)) sec^{7} (x) + 7 sec^{7} (x) tan (x) cos (x) : 6 sec^{7} (x) sin (x)

= 6 sec^{7} (x) sin (x)

What is the derivative of cos(xsec^7(x)) ?
The derivative of cos(xsec^7(x)) is 6sec^7(x)sin(x)
What is the first derivative of cos(xsec^7(x)) ?
The first derivative of cos(xsec^7(x)) is 6sec^7(x)sin(x)