If (F(x) = \integral\_{x^{2}}^{x^{3}}{\log tdt(x > 0)}), the... | MATH - DIFFERENTIATION OF IMPLICIT FUNCTION, PARAMETRIC AND COMPOSITE FUNCTIONS | SolveeIt

If $F(x) = \int_{x^{2}}^{x^{3}}{\log tdt(x > 0)}$ , then $F'(x)$ =

$(9x^{2} - 4x)\log x$

$(4x - 9x^{2})\log x$

$(9x^{2} + 4x)\log x$

None of these

Answer

$(9x^{2} - 4x)\log x$

Explanation

Applying formula we get $F'(x) = (\log x^{3})3x^{2} - (\log x^{2})2x$

= $(3\log x)3x^{2} - 2x(2\log x)$ = $9x^{2}\log x - 4x\log x$

= $(9x^{2} - 4x)\log x$ .

Question: If \(F(x) = \int_{x^{2}}^{x^{3}}{\log tdt(x > 0)}\), then \(F'(x)\) =...