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Popular >

derivative of sec(xtan(y))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

integral of 81-x^2

\int 81 - x^{2} d x

derivative of 3+x^{10}e^x

\frac{d}{d x} (3 + x^{10} e^{x})

integral of 1/(2^2+2x^2)

\int \frac{1}{2 ^{2} + 2 x ^{2}} d x

(dy)/(dx)=4xe^{(3y)}

\frac{d y}{d x} = 4 x e^{(3 y)}

integral of ((x+3)^2)/(sqrt(x))

\int \frac{( x + 3 ) ^{2}}{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of sec(xtan(y)) ?
The derivative of sec(xtan(y)) is sec(x)tan(x)tan(y)+sec^2(y)(dy)/(dx)sec(x)
What is the first derivative of sec(xtan(y)) ?
The first derivative of sec(xtan(y)) is sec(x)tan(x)tan(y)+sec^2(y)(dy)/(dx)sec(x)