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Differentiate sin x3 with respect to x3
- a)sin x3
- b)cos x3
- c)– cos x3
- d)– sin x3
Correct answer is option 'B'. Can you explain this answer?
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Differentiate sin x3with respect to x3a)sin x3b)cos x3c)– cos x3...
Differentiating sin(x^3) with respect to x^3:
To differentiate sin(x^3) with respect to x^3, we can use the chain rule of differentiation. The chain rule states that if we have a composite function, the derivative is equal to the derivative of the outer function multiplied by the derivative of the inner function.
Mathematically, let's represent sin(x^3) as f(g(x)), where g(x) = x^3 and f(x) = sin(x).
- The derivative of g(x) = x^3 with respect to x^3 is simply 1, as x^3 is the inner function.
- The derivative of f(x) = sin(x) with respect to x is cos(x), as it is a standard result from trigonometry.
Now we can apply the chain rule:
df(g(x))/dx = df(g(x))/dg(x) * dg(x)/dx
Substituting the values:
df(g(x))/dg(x) = df(g(x))/dx^3 = cos(x^3)
dg(x)/dx = dg(x)/dx^3 = 1
Therefore,
df(g(x))/dx = cos(x^3) * 1 = cos(x^3)
So, the correct answer is option 'B', which is cos(x^3).
To differentiate sin(x^3) with respect to x^3, we can use the chain rule of differentiation. The chain rule states that if we have a composite function, the derivative is equal to the derivative of the outer function multiplied by the derivative of the inner function.
Mathematically, let's represent sin(x^3) as f(g(x)), where g(x) = x^3 and f(x) = sin(x).
- The derivative of g(x) = x^3 with respect to x^3 is simply 1, as x^3 is the inner function.
- The derivative of f(x) = sin(x) with respect to x is cos(x), as it is a standard result from trigonometry.
Now we can apply the chain rule:
df(g(x))/dx = df(g(x))/dg(x) * dg(x)/dx
Substituting the values:
df(g(x))/dg(x) = df(g(x))/dx^3 = cos(x^3)
dg(x)/dx = dg(x)/dx^3 = 1
Therefore,
df(g(x))/dx = cos(x^3) * 1 = cos(x^3)
So, the correct answer is option 'B', which is cos(x^3).
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Differentiate sin x3with respect to x3a)sin x3b)cos x3c)– cos x3...
We know differe of sin x is cos x in respect to x but here is we do difffe with respect to x³ so sin x³ = cos x³
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Differentiate sin x3with respect to x3a)sin x3b)cos x3c)– cos x3d)– sin x3Correct answer is option 'B'. Can you explain this answer?
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