Differentiate x⁴(√sinx) with respect to x.

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

1. [B2] for ½ (sin x)⁻¹/² (cos x) oe (B1 for ½ (sin x)⁻¹/² or for (...)⁻¹/² x cos x or for their ½ (sin x)⁻¹/² x cos x)
2. [M1] Applies correct form of product rule (u'v + uv')
3. [A1] 4x³√sin x + x⁴ ½ (sin x)⁻¹/² (cos x) oe isw
4. [M1] Recognises that the integrand is of the form ∫(x + 2 * d/dx(x⁴√sin x))dx, or ∫[xdx+2(x⁴ cos x / (2√sin x) + 4x³ sin x)] dx oe (FT their (i))
5. [A2] x²/2 + 2x⁴√sin x [+c] (A1 for ∫x dx + 2x⁴√sin x or for x²/2 + 2x⁴√sin x)