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What is the derivative of x3 with respect to x2 ?
- a)3x2
- b)3x/2
- c)x
- d)3/2
Correct answer is option 'B'. Can you explain this answer?
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What is the derivative of x3 with respect to x2 ?a)3x2b)3x/2c)xd)3/2Co...
The derivative of x^3 with respect to x^2 can be found using the chain rule. The chain rule states that if we have a function f(g(x)), the derivative of f(g(x)) with respect to x is equal to the derivative of f(g(x)) with respect to g(x), multiplied by the derivative of g(x) with respect to x.
To find the derivative of x^3 with respect to x^2, we can treat x^2 as the variable and x^3 as the function. Let's denote x^2 as u and x^3 as f(u).
Derivative of x^3 with respect to x^2 (df(u)/du):
- To find the derivative of f(u) with respect to u, we can simply take the derivative of x^3 with respect to x, and then divide it by the derivative of u with respect to x.
- The derivative of x^3 with respect to x is 3x^2.
- The derivative of u (x^2) with respect to x is 2x.
Using the chain rule, the derivative of x^3 with respect to x^2 is:
df(u)/du = (3x^2) / (2x)
Simplifying the expression:
- We can cancel out one x from the numerator and denominator, resulting in:
df(u)/du = 3x / 2
Therefore, the correct answer is option 'B': 3x/2.
To find the derivative of x^3 with respect to x^2, we can treat x^2 as the variable and x^3 as the function. Let's denote x^2 as u and x^3 as f(u).
Derivative of x^3 with respect to x^2 (df(u)/du):
- To find the derivative of f(u) with respect to u, we can simply take the derivative of x^3 with respect to x, and then divide it by the derivative of u with respect to x.
- The derivative of x^3 with respect to x is 3x^2.
- The derivative of u (x^2) with respect to x is 2x.
Using the chain rule, the derivative of x^3 with respect to x^2 is:
df(u)/du = (3x^2) / (2x)
Simplifying the expression:
- We can cancel out one x from the numerator and denominator, resulting in:
df(u)/du = 3x / 2
Therefore, the correct answer is option 'B': 3x/2.
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