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11th Maths Weekly Test - 2 ( Differential Calculus - Differentiability and Methods of Differentiatio

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 2 ( Differential Calculus - Differentiability and Methods of Differentiatio-Aug 2020

Time : 1.30 Hours

Part - A

Generic 2 - Answer All Question

Differentiate the following:y = cos (tanx)

Find the derivation
(x⁴ - 6x³+ 7x² + 4x + 2) (x³ -1)

Differentiate x² (x + 1)³ (x + 2)⁴ with respect to' 'x'.

Find the derivatives of the following y = x^logx + (log x)^x

Find the derivatives of the following tan (x + y) + tan (x - y) = x

Find the derivation
3 sin x + 4 cos x - e^x

Show that the greatest integer function \(f(x)=\left\lfloor x \right\rfloor \) is not differentiable at any integer?

Find the derivatives of the following functions with respect to corresponding independent variables:f(x) = x sin x

Find the derivation
(3x² + 1)²

Differentiate the following with respect to x :\(y={log x \ x \over e^x}\)

Part - B

Generic 5 - Answer All Question

Find y' if x⁴+y⁴=16.

Differentiate x^x with respect to \(x\log { x } \)

If x = a (\(\theta\) + sin \(\theta\)), y = a (1 - cos \(\theta\)) then prove that at \(\theta={\pi\over 2},y"={1\over a}\)

If f(x) = |x + 100| + x², test whether f '(-100) exists.

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