Explain the answere of marked mcq's?how these option are correct?

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Answer 1 · 2017-08-18T03:19:35

I do not get those answers. Please see below.

#26)#

I don't understand the notation #d/dx = tan3x#

But #d/dx(tan3x) = sec^2 3x * d/dx(3x) = 3sec^2 3x#, which is closest to (A), but (A) still has the wrong argument.

I also do not understand the notation #sec^+ 3x#

#29)#

#f(g(x)) = sinx# and #g(x) = sqrtx#

Differentiating with respect to #x#, we get (using the chain rule)

#f'(g(x)) * g'(x) = cosx# and #g'(x) = 1/(2sqrtx)#

So #f'(g(x)) = 2sqrtx cosx# and

#f'(g(pi)) = f'(sqrtpi) = 2sqrtpi cospi = -2sqrtpi#

Which is choice (C).