Find the derivative of the given function.
$f(x)=\(\tan\)^{-1}(x^2)$

For problems 49–52 use implicit differentiation to find dy/dx at the given point P.

49. 3arctan(x) + arcsin(y) = π/4; P(1, -1)

For problems 49–52 use implicit differentiation to find dy/dx at the given point P.

51. y arccos(xy) = -3√2/4 π; P(1/2, -√2)

Find the derivative of the given function.

$f(x)=(x^3+4x)\(\sin\)^{-1}x$

Find the derivative of the given function.

$y=4\(\arccos\]\left\)(3x^6-x^5\(\right\))$

Find the derivative of the given function.

$f(t)=\(\csc\)^{-1}(2t+7)$

Find the derivative of the given function.

$f\(\left\)(x\(\right\))=\(\cot\)^{-1}\(\left\)(e^{\(\cos\) x}\(\right\))$

Find the slope of the line tangent to the graph of y = sin^−1 x at x=0.

Find the slope of the line tangent to the graph of y = tan^−1 x at x= −2.