Question

find dy/dx if y=(3a)^x+x^log3+x^a+a^a​

Answer 1

Answer:

The derivative of y with respect to x is: dy/dx = (3a)^x * ln(3a) + (log3) * x^(log3 - 1) + a * x^(a-1)

Step-by-step explanation:

To find the derivative of y with respect to x, we need to take the derivative of each term of y separately using the rules of differentiation.

y = (3a)^x + x^log3 + x^a + a^a

The derivative of the first term, (3a)^x, is:

d/dx [(3a)^x] = (3a)^x * ln(3a)

The derivative of the second term, x^log3, is:

d/dx [x^log3] = (log3) * x^(log3 - 1)

The derivative of the third term, x^a, is:

d/dx [x^a] = a * x^(a-1)

The derivative of the fourth term, a^a, is zero because it is a constant.

Putting all these derivatives together, we get:

dy/dx = (3a)^x * ln(3a) + (log3) * x^(log3 - 1) + a * x^(a-1)

Therefore, the derivative of y with respect to x is:

dy/dx = (3a)^x * ln(3a) + (log3) * x^(log3 - 1) + a * x^(a-1)

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