$Suppose\ f\ is\ differentiable\ on\ ℝ\ and\ F(x)=f(x^2+1)\ then\ F'(x)\ is:$

• A) $2xf'(2x)$
• B) $2xf' (x^2+1)$
• C) $f'(x^2+1)$
• D) $2x$

$If\ y=sin⁡(sin⁡(sinx))\ how\ many\ times\ chain\ rule\ will\ be\ applied\ to\ find\ y'.$

• A) 4
• B) 5
• C) 2
• D) 3

$Suppose\ f \ is\ differentiable\ on\ ℝ\ and\ F(x)=f(2x+1)\ then\ F'(x)\ is\ equal\ to:$

• A) $2$
• B) $2f'(2x+1)$
• C) $2f' (2)$
• D) $f'(2x+1)$

$If\ y=xe^{{x}^{2}}, f'(-2)\ is\ equal\ to:$

• A) $3e^{4}$
• B) $e^{4}$
• C) $-e^{4}$
• D) $9e^{4}$

$Suppose\ f\ is\ differentiable\ on\ ℝ\ and\ F(x)=(f(x^2 ))^2\ then\ F'(x)\ is\ equal\ to:$

• A) $4xf(x^2 )f'(x^2)$
• B) $2xf'(x^2)$
• C) $2f(x^2 ).f'(x^2)$
• D) $f'(x^2)f(x^2)$

$If\ f(1)=1, and\ f' (1)=-1,\ then\ \frac{d}{dx} (f(x^3 )f(x^2 )) \ at\ x=1.$

• A) $5$
• B) $-1$
• C) $1$
• D) $-5$

$Suppose\ f \ is\ differentiable\ on\ ℝ\ and\ F(x)=f(x^2 ) \ then\ F'(x)\ is\ equal\ to:$

• A) $f'(x^2)$
• B) $2x\ f' (x^2 )$
• C) $2xf'(x)$
• D) $2x$

$Suppose\ f\ is\ differentiable\ on\ ℝ\ and\ F(x)=(f(x))^2\ then\ F'(x)\ is\ equal\ to:$

• A) $2f(x)f'(x)$
• B) $2xf'(x^2)$
• C) $2xf' (x)$
• D) $f'(x)$

$If\ f(1)=1\ , f' (1)=2 \ then\ \frac{d}{dx} (e^{f(x^2)}) \ at\ x=1\ is:$

• A) $-2e$
• B) $-4e$
• C) $4e$
• D) $2e$

Suppose\ f \ is\ differentiable\ on\ ℝ\ and\ F(x)=f(2x+1)\ then\ F'(x)\ is\ equal\ to:

• A) f'(2x+1)
• B) 2f' (2)
• C) 2f'(2x+1)
• D) 2

Suppose\ f \ is\ differentiable\ on\ ℝ\ and\ F(x)=f(x^2 ) \ then\ F'(x)\ is\ equal\ to:

• A) 2x\ f' (x^2 )
• B) 2x
• C) 2xf'(x)
• D) f'(x^2)

Suppose\ f\ is\ differentiable\ on\ ℝ\ and\ F(x)=(f(x^2 ))^2\ then\ F'(x)\ is\ equal\ to:

• A) f'(x^2)f(x^2)
• B) 2xf'(x^2)
• C) 2f(x^2 ).f'(x^2)
• D) 4xf(x^2 )f'(x^2)

If\ f(1)=1, and\ f' (1)=-1,\ then\ \frac{d}{dx} (f(x^3 )f(x^2 )) \ at\ x=1.

• A) -1
• B) 1
• C) 5
• D) -5

If\ y=xe^{{x}^{2}}, f'(-2)\ is\ equal\ to:

• A) e^{4}
• B) 3e^{4}
• C) -e^{4}
• D) 9e^{4}

If\ f(1)=1\ , f' (1)=2 \ then\ \frac{d}{dx} (e^{f(x^2)}) \ at\ x=1\ is:

• A) -2e
• B) 2e
• C) 4e
• D) -4e

Suppose\ f\ is\ differentiable\ on\ ℝ\ and\ F(x)=(f(x))^2\ then\ F'(x)\ is\ equal\ to:

• A) f'(x)
• B) 2f(x)f'(x)
• C) 2xf' (x)
• D) 2xf'(x^2)

If\ y=sin⁡(sin⁡(sinx))\ how\ many\ times\ chain\ rule\ will\ be\ applied\ to\ find\ y'.

• A) 2
• B) 3
• C) 5
• D) 4

\(Suppose\ f \ is\ differentiable\ on\ ℝ\ and\ F(x)=f(x^2 ) \ then\ F'(x)\ is\ equal\ to:\)

• A) \(f'(x^2)\)
• B) \(2x\ f' (x^2 )\)
• C) \(2x\)
• D) \(2xf'(x)\)

\( If\ y=xe^{{x}^{2}}, f'(-2)\ is\ equal\ to: \)

• A) \(-e^{4} \)
• B) \(3e^{4}\)
• C) \(9e^{4} \)
• D) \( e^{4}\)

Suppose\ f\ is\ differentiable\ on\ ℝ\ and\ F(x)=f(x^2+1)\ then\ F'(x)\ is:

• A) 2x
• B) f'(x^2+1)
• C) 2xf'(2x)
• D) 2xf' (x^2+1)