Chain rules, tangent, and Normal

Chain rules, tangent, and Normal

Mr. U_Ir

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Remember how to differentiate

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Multiple Choice

Find the derivative of  $3x^7-x^3+3x-1$  

•  $3x^7-x^3+3x-1$  

•  $21x^6-3x^2+3x-1$  

•  $21x^6-3x^2+3$  

•  $21x^7-3x^3+3x-1$  

Multiple Choice

Find the derivative of $\frac{1}{x^7}$  

•  $-\frac{1}{7x^6}$  

•  $\frac{1}{7x^6}$  

•  $-\frac{7}{x^8}$  

•  $\frac{7}{x^8}$  

Multiple Choice

Find the derivative of  $\frac{4}{\sqrt{x}}$  

•  $\frac{2}{\sqrt{x}}$  

•  $-\frac{2}{\sqrt{x^3}}$  

•  $\frac{2}{\sqrt{x^3}}$  

•  $-\frac{2}{\sqrt{x}}$  

Chain rules

Prepare your note

Multiple Choice

Find the derivative of $y=\left(2x^2-1\right)^5$  

•  $y'=5\left(2x^2-1\right)^4$  

•  $y'=5\left(4x-1\right)^4$  

•  $y'=20x\left(2x^2-1\right)^4$  

•  $y'=20x\left(4x-1\right)^4$  

Multiple Choice

Find the gradient of tangent to curve $y=\frac{1}{\left(3x^2-2\right)^5}$  at the point where x=1 

•  $-5$  

•  $-6$  

•  $1$  

•  $-30$  

Tangent line

The gradient of tangent is the derivative of the curve

Multiple Choice

Find the point of tangency of tangent line to curve $y=\frac{1}{\left(3x^2-2\right)^5}$  at the point where x=1 

•  $\left(1,1\right)$  

•  $\left(1,-1\right)$  

•  $\left(-1,1\right)$  

•  $\left(-1,-1\right)$  

Multiple Choice

Find the equation of tangent line to curve $y=\frac{1}{\left(3x^2-2\right)^5}$  at the point where x=1 

•  $y-1=-60\left(x-1\right)$  

•  $y-1=60\left(x-1\right)$  

•  $y+1=-60\left(x-1\right)$  

•  $y+1=60\left(x-1\right)$  

Multiple Choice

Find the equation of tangent to the curve  $y=2x^2+\frac{8}{x^2}-9$  at the point where x = 2.

•  $y=6x-11$  

•  $y=6x+11$  

•  $y=-6x-11$  

•  $y=-6x+11$  

Normal line

The line which perpendicular to the tangent line

Multiple Choice

Find the gradient of normal to curve $y=\frac{1}{\left(3x^2-2\right)^5}$  at the point where x=1 

•  $\frac{1}{30}$  

•  $30$  

•  $-\frac{1}{30}$  

•  $-30$  

Multiple Choice

Find the equation of normal line to curve $y=\frac{1}{\left(3x^2-2\right)^5}$  at the point where x=1 

•  $y-1=-\frac{1}{60}\left(x-1\right)$  

•  $y-1=\frac{1}{60}\left(x-1\right)$  

•  $y+1=-\frac{1}{60}\left(x-1\right)$  

•  $y+1=\frac{1}{60}\left(x-1\right)$  

Multiple Choice

Find the equation of normal to the curve  $y=2x^2+\frac{8}{x^2}-9$  at the point where x = 2.

•  $x+6y=-8$  

•  $x+6y=8$  

•  $6x+y=-8$  

•  $6x+y=8$  

Poll

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Mr. U_Ir