What is the derivative of x*tan(x^2) ?

The derivative of x*tan(x^2) is tan(x^2)+2x^2sec^2(x^2)

What is the first derivative of x*tan(x^2) ?

The first derivative of x*tan(x^2) is tan(x^2)+2x^2sec^2(x^2)

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\frac{d}{d x} (x \cdot tan (x^{2}))

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = tan (x^{2})

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

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

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

= 1 \cdot tan (x^{2}) + sec^{2} (x^{2}) \cdot 2 xx

Simplify

1 \cdot tan (x^{2}) + sec^{2} (x^{2}) \cdot 2 xx : tan (x^{2}) + 2 x^{2} sec^{2} (x^{2})

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

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