Question

Differentiate the following functions with respect to x (i) sinh x tanh x (ii) Z x √ x sin t t dt.

Answer 1

(i) $\sinh x\tanh x$

differentiating with respect to x

$=\tanh x(\cosh x)+\sinh x(sec h^2x)$

$=\sinh x+\sinh x(sech^2 x)$

(ii) $Zx\sqrt{x}\sin t \space tdt$

treating Z and t as constant and differentiating with respect to x

$=\dfrac{3}{2}x^{\frac{3}{2}-1}Z\sin t\space tdt$

$=\dfrac{3}{2}x^{\frac{1}{2}}Z\sin t\space tdt$