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To differentiate y, we must used the product rule.The product rule is d/dx [f(x)g(x)] = f'(x)g(x) + g'(x)f(x)So here, we let f(x)= x^3 and g(x)= sin(x)Then, f'(x)= 3x^2 and g'(x) = cos(x)Then substituting...
Here we can use the product rule where dy/dx = v du/dx + u dv/dx.We let u = x and v = (4x + 1)1/2 which means we get du/dx = 1 and by using the chain rule we get dv/dx = 1/2(4x + 1)-1/2RNAnswered by Rebecca N. • Maths tutor5866 Views
6cos(2x) +sin(x).Using the double angle formula for cosine (or otherwise), cos(2x) = cos(x)cos(x) - sin(x)sin(x) .cos(2x) = cos^2(x) - sin^2(x) .Hence, 6cos(2x) +sin(x) = 6(cos^2(x) - sin...
The first part of the problem is solved by differentiating once and equating this to zero:y = x^3 - 3x^2 +4 .dy/dx = 3x^2 - 6x .dy/dx = x(3x - 6...
The answer can be found by using the chain rule and simple substitution as well as basic knowledge of differentiation.f’(x)= -6cos(3x)sin(3x)
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