Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

Check for the derivative of sin x with respect to cos x is –cot x or not. Then write 1 if true and 0 if false.

Answer
VerifiedVerified
536.4k+ views
like imagedislike image
Hint – In this question let y = sin x and z = cos x, then find dydx and dzdx, use these obtained derivatives to find the value of dydz. If it comes out equal to –cot x, then the answer is 1 else 0.

Complete step-by-step solution -
Let y = sin x...................... (1)
And z = cos x........................ (2)
Now differentiate equation (1) w.r.t. x we have,
dydx=ddxsinx=cosx.................. (3)
Now differentiate equation (2) w.r.t. x we have,
dzdx=ddxcosx=sinx........................ (4)
Now divide equation (3) from equation (4) we have,
dydxdzdx=cosxsinx
Now as we know that (cos/sin) = cot so we have,
dydz=cosxsinx=cotx
So this is the required differentiation of sin x w.r.t. cos x.
And the required answer is (-cot x).
So the given statement is true.
So according to the question we have to write 1.
So this is the required answer.

Note – This method is used to find the derivative of one entity with respect to another entity by taking the derivative of individual entities, and is most commonly used to solve any derivative problem of this kind. It is advised to remember the derivative of basic trigonometric ratios like sin x, cos x, tan x, cot x as it helps saving a lot of time.

Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
PhysicsPhysics
ChemistryChemistry
MathsMaths
₹41,848 per year
EMI starts from ₹3,487.34 per month
Select and buy