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Given y=f(x) then df/dx is given by which of the following? 1. 2. 3. 4.
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equals 1.-2sin2x 2.-sin(2x) 3.0 4.-2xsin2x
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If y=x n then find dy/dx 1.nx n 2.nx n-1 3.x n-1 4.(n-1)x n
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Find the derivative of f(x)=3x³-½x²+5x+1 with respect to x 1.9x² – 2x + 5 2.9x³ – x² + 5x + 1 3.9x² – x + 5 4.9x³ – x² + 6
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If 1.-3e 3x 2.3e 3x 3.-3e 2x 4.-3xe 2x
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f(k)=tan3k, find 1.3sec3k 2.sec3k 3.3sec²3k 4.sec²3k
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= 1.sin(x) 2.-sin(x) 3.cos(x) 4.-cos(x) 5.cosec(x) John Goodband, Coventry University
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= 1. 2. 3. 4. 5.
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= John Goodband, Coventry University 1. 2. 3. 4. 5.
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Find the derivative of 1. 2. 3. 4. with respect to x
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Find the derivative of z = 2sint – cos2t with respect to t 1.2cost + sin2t 2.2cost – sin 2t 3.2cost + 2sin2t 4.2cost – 2sin2t
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If then 1. 2. 3. All of the above 4.
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1.The derivatie of f(x)+g(x) is 2.The derivative of f(x)-g(x) is 3.If k is constant, the derivative of kf(x) is 4.If y=f(x)g(x) then Which of the following statements are true?
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equals 1.2-e cosx sinx +2xcos2x 2.x+ e cosx +2cos2x 3.2-e cosx sinx +2cos2x 4.Not enough information
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Find the derivative of y=2xe -x with respect to x 1.-2xe -x + 2e -x 2.-2xe -x + 2e -x 3.2xe -x – 2e -x 4.2xe -x + 2e -x
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Find the derivative of y=(e 2x ) 6 with respect to x 1.6e 2x 2.12e 12x 3.12xe x 4.12e x
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= John Goodband, Coventry University 1.2xcos(x²) 2.cos(x²) 3.2xcos(x) 4.x²cos(x²) + 2xsin(x²)
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Which of the following is the quotient rule if ? 1. 2. 3. 4.
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Use the quotient rule to find the derivative of f(x)=x -3 cosx with respect to x 1. 2. 3. 4.
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We know and. Then equals: 1.5/2 2.7/2 3.3
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Using the chain rule, find the derivative f(x)=(3x²+2)² with respect to x 1.2(3x² + 2) 2.12(3x + 2) 3.12x(3x² + 2) 4.12x + 4
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Suppose a runner has a speed of 8 miles per hour, while a cyclist has a speed of 16 miles per hour. Then dV/dt for the cyclist is 2 times greater than dV/dt for the runner. This is explained by: 1.The chain rule 2.The product rule 3.The quotient rule 4.The addition rule
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The radius of a balloon changes as it deflates. This change in radius with respect to volume is: 1. 2. 3. None of these 4.
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Calculate the second derivative of y = 4x³ – 2x + x² – 3 with respect to x 1.24x + 2 2.24x – 2x 3.12x – 2 4.12x² – 2 +2x
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If then find 1. 2. 3. 4.
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If x=h(t) and y=g(t) then 1. 2. 3. 4.
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Find the value of if x=3t 2 and y=2t-1. 1. 2. 3. 4.
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1. If x=h(t) and y=g(t) then 2. 3. 4.
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Find the equation of the tangent line to the curve x=1-3sint, y=2+cost at. 1. 2. 3. None of the above 4.
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Which differentiation rule is needed to differentiate implicit functions? 1.Product rule 2.Chain rule 3.Quotient rule 4.Inverse function rule
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Find if 3y=xy+siny. 1. 2. 3. 4.
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Find at the point (3,1) on x 2 +2xy+y 2 =x. 1. 2. 3. 4.
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