What is the derivative of xtan(y) ?

The derivative of xtan(y) is tan(y)+xsec^2(y)(dy)/(dx)

What is the first derivative of xtan(y) ?

The first derivative of xtan(y) is tan(y)+xsec^2(y)(dy)/(dx)

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = tan (y)

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

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

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

= 1 \cdot tan (y) + sec^{2} (y) \frac{d y}{d x} x

Simplify

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

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