Differentiation — Mathematics

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Question 1
EasyJEE

Ify=ax(a>0),thendy/ dx=If y = aˣ (a>0), then dy/\,dx =

A. axln⁡(a)aˣ \ln(a)
B. xax−1x a^{x-1}
C. aˣ
D. ax/ln⁡(a)aˣ / \ln(a)
Question 2
MediumJEE

Ify=log⁡10(x),thendy/ dx=If y = \log₁₀(x), then dy/\,dx =

A. 1/(xln⁡10)1/(x \ln 10)
B. 1/x1/x
C. ln⁡10/x\ln 10 / x
D. 1/(xlog⁡10e)1/(x \log₁₀ e)
Question 3
EasyJEE

Ify=sin⁡−1(x),thendy/ dx=If y = \sin⁻¹(x), then dy/\,dx =

A. 1/1−x21/\sqrt{1-x²}
B. 1/1+x21/\sqrt{1+x²}
C. 1/(1+x2)1/(1+x²)
D. 1/(1−x2)1/(1-x²)

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