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Given that y = 5x^(3) + 7x + 3, find dy/dx

(i): 15x^(2)+7 --- in order to arrive at this answer, we can divide the equation into 3 separate parts: 5x^(3) and 7x and 3. For the first part, you would multiply the first number, 5 by the power, in this c...
AP
Answered by Angela P. • Maths tutor
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What is the gradient of the function y=x^3 at the point x=1?

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KS
Answered by Kiran S. • Maths tutor
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A curve C has the equation x^3 + 6xy + y^2 = 0. Find dy/dx in terms of x and y.

By differentiating with respect to x, 3x^2+6x(dy/dx)+6y+2y(dy/dx)=0 So, dy/dx(6x+2y)=-3x^2-6y so dy/dx = -(3x^2+6y)/(2(3x+y))
MH
Answered by Mike H. • Maths tutor
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Why does adding a constant to a function's input (as in f(x-a)) shift the plot of the function along the x-axis?

Imagine the function f(x) as a black box which takes in any value x and produces an output y. The black box acts on its input according to a rule which produces a unique value of y for a given x. If the blac...
JH
Answered by James H. • Maths tutor
7785 Views

Solve the following definite integral: f(x)=3e^(2x+1) for the limits a=0 and b=1, leaving your answer in exact form.

First set up integral. Do not forget dx! Int(f(x)) between 0 and 1 Optionally take out factor of 3 to simplify problem. Solve using substitution and the exponential rule. Integrated function should be (3/2)e...
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Answered by Fraser B. • Maths tutor
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