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Solve the simultaneous equations: y=x^2 + 3x + 7 and y=x + 10

x= -3 and 1y= 7 and 11

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Differentiate the following equation: f(x) = 5x^3 + 6x^2 - 12x + 4

Answer:
f'(x) = 15x^2 + 12x -12
This is according to basic rules of differentiation and is a beginner level differentiation question as following:If f(x) = ax^nThen f'(x) = x(nx^n-1)

Answered by Holly K. • Maths tutor

2710 Views

Differentiate 5x^3 + 4x^2 + 5x + 9

Differentiate 5x³ + 4x² + 5x + 9The rules from polynomial differentiation: d(axⁿ) / dx= a(nx^n-1) and df/dx + dg/dx = d (f+g) /dx and dn/dx = 0Using these rules...

Answered by Annabelle S. • Maths tutor

3253 Views

A curve has equation 3x^4/3-16y^3/4=32. By differentiating implicitly find dy/dx in terms of x and y. Hence find the gradient of the curve at the point (8,1).

3x^4/3-16y^3/4=32Differentiating implicitly:4x^1/3-12y^-1/4(dy/dx)=0Simplifying and rearranging:x^1/3=3y^-1/4(dy/dx)dy/dx=1/3(x^1/3y

Answered by Ben G. • Maths tutor

3194 Views

How do you make f the subject of the following a = c/d + e/f

1)Multiply out the right hand side to give a common denominator: a= (Cf+de)/df2) Cross multiply to get rid of the denominator fda = cf + de3) bring all terms containing f to the same side and factorise fd...

Answered by Kwaku D. • Maths tutor

2731 Views