If u- v and w are functions of x- then show that d-d xu - v - w-d u-d x v - w-u -d v-d x - w-u - v -d w-d xin two ways-first by repeated application of product rule- second by logarithmic differentiation-

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Standard XII

Mathematics

Statement

If u, v and w...

Question

If u, v and w are functions of x, then show that

in two ways-first by repeated application of product rule, second by logarithmic differentiation.

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Solution

Let

By applying product rule, we obtain

By taking logarithm on both sides of the equation, we obtain

Differentiating both sides with respect to x, we obtain

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If u, v and w are functions of x, then show that in two ways-first by repeated application of product rule, second by logarithmic differentiation.

Let By applying product rule, we obtain By taking logarithm on both sides of the equation, we obtain Differentiating both sides with respect to x, we obtain

If u, v and w are functions of x, then show that

in two ways-first by repeated application of product rule, second by logarithmic differentiation.

Let

By applying product rule, we obtain

By taking logarithm on both sides of the equation, we obtain

Differentiating both sides with respect to x, we obtain