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Find the derivate of y = sin4x + cos4x
- a)– sin 2x
- b)4 sin3 x + 4 cos3 x
- c)– sin 4x
- d)4 sin x cos x cos 2x
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Find the derivate of y = sin4x + cos4xa)– sin 2xb)4 sin3x...
Derivative of y = sin4x + cos4x
- To find the derivative of y = sin4x + cos4x, we need to apply the chain rule.
- The derivative of sin4x is 4cos4x (using the chain rule) and the derivative of cos4x is -4sin4x (using the chain rule).
- Therefore, the derivative of y = sin4x + cos4x is 4cos4x - 4sin4x.
- Simplifying further, we get the derivative as 4(cos4x - sin4x).
Therefore, the correct answer is option C. sin 4x.
- To find the derivative of y = sin4x + cos4x, we need to apply the chain rule.
- The derivative of sin4x is 4cos4x (using the chain rule) and the derivative of cos4x is -4sin4x (using the chain rule).
- Therefore, the derivative of y = sin4x + cos4x is 4cos4x - 4sin4x.
- Simplifying further, we get the derivative as 4(cos4x - sin4x).
Therefore, the correct answer is option C. sin 4x.
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Community Answer
Find the derivate of y = sin4x + cos4xa)– sin 2xb)4 sin3x...
y=sin4x, and z=cos4x
So by using chain rule
df(x)/dx = dsin4x/dx + dcos4x/dx
=dy4/dy * dy/dx + dz4/dz * dzdx
=dy4/dy * dsinxdx + dz4/dz * dcosx/dx
=4y(4−1)⋅cosx+4z(4−1)⋅(−sinx)
=4sin3xcosx − 4cos3xsinx
=4sinxcosx(sin2x − cos2x)
=2sin2x(−cos2x)
=−2sin2xcos2x
=−sin4x
So by using chain rule
df(x)/dx = dsin4x/dx + dcos4x/dx
=dy4/dy * dy/dx + dz4/dz * dzdx
=dy4/dy * dsinxdx + dz4/dz * dcosx/dx
=4y(4−1)⋅cosx+4z(4−1)⋅(−sinx)
=4sin3xcosx − 4cos3xsinx
=4sinxcosx(sin2x − cos2x)
=2sin2x(−cos2x)
=−2sin2xcos2x
=−sin4x
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Find the derivate of y = sin4x + cos4xa)– sin 2xb)4 sin3x + 4 cos3xc)– sin 4xd)4 sin x cos x cos 2xCorrect answer is option 'C'. Can you explain this answer?
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