Question

differentiate cos x^3.sin^2(x^5)with respect to x​

Answer 1

$Let -$

$\cos(x) {}^{3} \cdot \sin {}^{2} (x^{5} ) = f(x)$

$To \: find : f' (x)$

$Differentiate \: the \: function \: on \: both \: the \: sides \: w.r.t \: x$

$f'(x) = d( \cos \: x^{3} ) \cdot \: { \sin }^{2} ( {x}^{5} ) + d( \sin {}^{2} ( {x}^{5} ) \cdot \: \cos( {x}^{3} )$

$Differentiate the \cos \: x^{3} and { \sin}^{x} {x}^{5} \: w.r.t \: x.$

$\green{f'(x) = - \sin( {x}^{3} ) \cdot \: 3 {x}^{2} \cdot \: { \sin }^{2} ( {x}^{5} ) + 2 \sin( {x}^{5} ) \cdot \: 5 {x}^{4} \cdot \: \cos{x}^{3}}$