Question

Choose the correct alternative.

If y = 5^x . x⁵, then `"dy"/"dx" = ?` 

Options

• 5^x. x⁴ (5 + log 5)

• 5^x. x⁵ (5 + log 5)

• 5^x . x⁴ (5 + x log 5)

• 5^x. x⁵ (5 + x log 5)

Answer 1

5^x . x⁴ (5 + x log 5)

Explanation:

y = 5^x . x⁵

Differentiating both sides w.r.t.x, we get

`"dy"/"dx" = 5^"x" * "d"/"dx" ("x"^5) + "x"^5 * "d"/"dx" (5^"x")`

`= 5^"x" * (5"x"^4) + "x"^5 (5^"x" * log 5)`

`= 5^"x" * "x"^4(5 + "x" log 5)`