11th Maths Weekly Test - 4 (Differential Calculus - Differentiability and Methods of Differentiation

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 4 (Differential Calculus - Differentiability and Methods of Differentiation-Aug 2020

Time : 1.30 Hours

Part - A

Generic 3 - Answer All Question

Differentiate \(f\left( x \right) ={ e }^{ 2x }\)from first principles.

Find the derivatives of the following functions with respect to corresponding independent variables:\(y={tan \ x-1\over sec \ x}\)

Show that the following functions are not differentiable at the indicated value of x.
f(x) = \(\begin{cases} 3x, & x<0 \\ -4x & x\ge 0 \end{cases};\) x=0

Find the derivatives of the following functions with respect to corresponding independent variables:\(y={tan \ x \over x}\) .

Differentiate the following:y=\(\\ xe^{ { -x }^{ 2 } }\) .

Differentiate the following:y=tan(cos x)

Determine whether the following function is differentiable at the indicated values. f(x) = |x| + |x - 1| at x = 0, 1

If \({ x }^{ 2 }+2xy+{ y }^{ 3 }=42,\quad find\quad \frac { dy }{ dx } \)

Find the derivatives of the following\(tan^{-1}({6x\over 1-9x^2})\)

Show that f(x) = x² is differentiable at x = 1 and find f'(1).

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11th Maths Weekly Test - 4 (Differential Calculus - Differentiability and Methods of Differentiation

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 4 (Differential Calculus - Differentiability and Methods of Differentiation-Aug 2020

Part - A

Generic 3 - Answer All Question

Differentiate \(f\left( x \right) ={ e }^{ 2x }\)from first principles.

Find the derivatives of the following functions with respect to corresponding independent variables:\(y={tan \ x-1\over sec \ x}\)

Show that the following functions are not differentiable at the indicated value of x. f(x) = \(\begin{cases} 3x, & x<0 \\ -4x & x\ge 0 \end{cases};\) x=0

Find the derivatives of the following functions with respect to corresponding independent variables:\(y={tan \ x \over x}\) .

Differentiate the following:y=\(\\ xe^{ { -x }^{ 2 } }\) .

Differentiate the following:y=tan(cos x)

Determine whether the following function is differentiable at the indicated values. f(x) = |x| + |x - 1| at x = 0, 1

If \({ x }^{ 2 }+2xy+{ y }^{ 3 }=42,\quad find\quad \frac { dy }{ dx } \)

Find the derivatives of the following\(tan^{-1}({6x\over 1-9x^2})\)

Show that f(x) = x2 is differentiable at x = 1 and find f'(1).

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Show that the following functions are not differentiable at the indicated value of x.
f(x) = \(\begin{cases} 3x, & x<0 \\ -4x & x\ge 0 \end{cases};\) x=0

Show that f(x) = x² is differentiable at x = 1 and find f'(1).