What is the derivative of xsec(y) ?

The derivative of xsec(y) is sec(y)+xsec(y)tan(y)(dy)/(dx)

What is the first derivative of xsec(y) ?

The first derivative of xsec(y) is sec(y)+xsec(y)tan(y)(dy)/(dx)

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = sec (y)

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

\frac{d x}{d x} = 1

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

= 1 \cdot sec (y) + sec (y) tan (y) \frac{d y}{d x} x

Simplify

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

\frac{1}{x - 4}

\int_{0}^{4} (x - (x - 2)) d x

y = \frac{- 10}{x ^{4}}

\frac{d}{d t} (2 t)

\frac{d y}{d x} = y^{2} e^{x} sin (3 x), y (0) = 1

What is the derivative of xsec(y) ?
The derivative of xsec(y) is sec(y)+xsec(y)tan(y)(dy)/(dx)
What is the first derivative of xsec(y) ?
The first derivative of xsec(y) is sec(y)+xsec(y)tan(y)(dy)/(dx)