Question
Diffrentiate the following w.r.t.x
$\sec \left[\tan \left(x^4+4\right)\right]$
$\sec \left[\tan \left(x^4+4\right)\right]$
Differentiating w.r.t. x, we get
$\begin{aligned} & \frac{d y}{d x}=\frac{d}{d x}\left\{\sec \left[\tan \left(x^4+4\right)\right]\right\} \\ & =\sec \left[\tan \left(x^4+4\right)\right] \cdot \tan \left[\tan \left(x^4+4\right)\right] \cdot \frac{d}{d x}\left[\tan \left(x^4+4\right)\right] \\ & =\sec \left[\tan \left(x^4+4\right)\right] \cdot \tan \left[\tan \left(x^4+4\right)\right] \cdot \sec ^2\left(x^4+4\right) \cdot \frac{d}{d x}\left(x^4+4\right) \\ & =\sec \left[\tan \left(x^4+4\right)\right] \cdot \tan \left[\tan \left(x^4+4\right)\right] \cdot \sec ^2\left(x^4+4\right)\left(4 x^3+0\right) \\ & =4 x^3 \sec ^2\left(x^4+4\right) \cdot \sec \left[\tan \left(x^4+4\right)\right] \cdot \tan \left[\tan \left(x^4+4\right)\right]\end{aligned}$
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$(\bar{a}+\bar{b}+\bar{c}) \times \bar{c}+(\bar{a}+\bar{b}+\bar{c}) \times \bar{b}+(\bar{b}+\bar{c}) \times \bar{a}=2 \bar{a} \times \bar{c}$
Question is modified.
For any vectors $\bar{a}, \bar{b}, \bar{c}$ show that
$(\bar{a}+\bar{b}+\bar{c}) \times \bar{c}+(\bar{a}+\bar{b}+\bar{c}) \times \bar{b}+(\bar{b}-\bar{c}) \times \bar{a}$
$=2 \bar{a} \times \bar{c}$.
$x=a t^2, y=2 a t$