If $ y=\left|\begin{array}{ccc}f(x) & g(x) & h(x) \ l & m & n \ a & b & c\end{array}\right| $, then $ \frac{d y}{d x} $ is equal to

Question

If $ y=\left|\begin{array}{ccc}f(x) & g(x) & h(x) \ l & m & n \ a & b & c\end{array}\right| $, then $ \frac{d y}{d x} $ is equal to, $ \left|\begin{array}{ccc}f^{\prime}(x) & g^{\prime}(x) & h^{\prime}(x) \ l & m & n \ a & b & c\end{array}\right| $, $ \left|\begin{array}{ccc}l & m & n \ f^{\prime}(x) & g^{\prime}(x) & h^{\prime}(x) \ a & b & c\end{array}\right| $, $ \left|\begin{array}{lll}f^{\prime}(x) & l & a \ g^{\prime}(x) & m & b \ h^{\prime}(x) & n & c\end{array}\right| $, $ \left|\begin{array}{ccc}l & m & n \ a & b & c \ f^{\prime}(x) & g^{\prime}(x) & h^{\prime}(x)\end{array}\right| $

MARKS App · Accepted Answer

Given that, $ y=\left|\begin{array}{ccc}f(x) & g(x) & h(x) \ l & m & n \ a & b & c\end{array}\right| $ So, $ \frac{d y}{d x}=\left|\begin{array}{ccc}f^{\prime}(x) & g^{\prime}(x) & h^{\prime}(x) \ l & m & n \ a & b & c\end{array}\right|+\left|\begin{array}{ccc}f(x) & g(x) & h(x) \ 0 & 0 & 0 \ a & b & c\end{array}\right|+ $ $ \left|\begin{array}{ccc}f(x) & g(x) & h(x) \ l & m & n \ 0 & 0 & 0\end{array}\right| $ $ =\left|\begin{array}{ccc}f^{\prime}(x) & g^{\prime}(x) & h^{\prime}(x) \ l & m & n \ a & b & c\end{array}\right| $

Search any question & find its solution

Looking for more such questions to practice?