Determine the first derivative (dy/dx) of y= tan (3x^2)

Question

Determine the first derivative $(\frac{d y}{d x}) o f y = \tan (3 x^{2})$

Answer 1

Determine the first derivative $(d y / d x) o f y = \tan (3 x^{2})$
Let $u = 3 x^{2}$ , then
$y = \tan (u)$
And, $\frac{d y}{d x} = (\frac{d y}{d u}) \cdot (\frac{d u}{d x})$
Taking $y = \tan (u)$ , then $\frac{d y}{d u} = \sec^{2} (u)$
Taking $u = 3 x^{2}$ , then $\frac{d u}{d x} = 6 x$
So, $\frac{d y}{d x} = (\frac{d y}{d u}) \cdot (\frac{d u}{d x})$
$\frac{d y}{d x} = (\sec^{2} (u)) \cdot (6 x)$
$\frac{d y}{d x} = 6 x \cdot \sec^{2} (3 x^{2})$

Determine the first derivative (dy/dx) of y= tan (3x^2)

Expert Answer

Not exactly what you’re looking for?

Relevant Questions