(d/dx)(x√a2-x2+a2 sin-1((x/a))) is equal to

Question

(d/dx)(x√a2-x2+a2 sin-1((x/a))) is equal to (A) √a2-x2 (B) 2√a2-x2 (C) (1/√a2-x2) (D) none of these

Tardigrade Admin · Accepted Answer

(d/dx) x√a2-x2+a2 sin-1((x/a)) =(x × 1 × (-2x)/2√a2-x2)+√a2-x2+a2 (1/√1-(x2)a2) ×(1/a) =(-x2/√a2-x2)+√a2-x2+(a2/a2-x2) =√a2-x2+((a2-x2)/√a2-x2) =2√a2-x2

Q. $\frac{d}{d x} (x a^{2} - x^{2} + a^{2} s i n^{- 1} (\frac{x}{a}))$ is equal to

$a^{2} - x^{2}$

$2 a^{2} - x^{2}$

$\frac{1}{a ^{2} - x ^{2}}$

none of these

Q. dxd​(xa2−x2​+a2sin−1(ax​)) is equal to

a2−x2​

2a2−x2​

a2−x2​1​

none of these

dxd​{xa2−x2​+a2sin−1(ax​)} =2a2−x2​x×1×(−2x)​+a2−x2​+a21−a2x2​​1​×a1​ =a2−x2​−x2​+a2−x2​+a2−x2a2​ =a2−x2​+a2−x2​(a2−x2)​ =2a2−x2​

Q. $\frac{d}{d x} (x a^{2} - x^{2} + a^{2} s i n^{- 1} (\frac{x}{a}))$ is equal to

$a^{2} - x^{2}$

$2 a^{2} - x^{2}$

$\frac{1}{a ^{2} - x ^{2}}$