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Popular >

Find the Derivative - d/dx tan(x)sec(x)

Solution

derivative of

\frac{d}{d x} (tan (x) sec (x))

Solution

- sec (x) + 2 sec^{3} (x)

Solution steps

\frac{d}{d x} (tan (x) sec (x))

Apply the Product Rule:

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

f = tan (x), g = sec (x)

= \frac{d}{d x} (tan (x)) sec (x) + \frac{d}{d x} (sec (x)) tan (x)

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

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

= sec^{2} (x) sec (x) + sec (x) tan (x) tan (x)

Simplify

sec^{2} (x) sec (x) + sec (x) tan (x) tan (x) : - sec (x) + 2 sec^{3} (x)

= - sec (x) + 2 sec^{3} (x)

Popular Examples

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\frac{d}{d x} ((\frac{50}{( x )}) x)

Evaluate the Limit limit as h approaches 0 of ((x+h)^4-x^4)/h

h \to 0 lim \frac{( ( x + h ) ^{4} - x ^{4} )}{h}

Find the Derivative - d/dx 100/(100-x)derivative of

\frac{d}{d x} (\frac{100}{( 100 - x )})

Find the Slope (4,0) , (0,4)slope

(4, 0), (0, 4)

Evaluate the Integral integral of tan(y) with respect to y

\int (tan (y)) d y

Frequently Asked Questions (FAQ)

What is the derivative derivative of tan(xsec(x)) ?
The derivative derivative of tan(xsec(x)) is -sec(x)+2sec^3(x)
What is the first derivative derivative of tan(xsec(x)) ?
The first derivative derivative of tan(xsec(x)) is -sec(x)+2sec^3(x)