In the second last line, it is not clear where 23x^4 appeared from. Also, in the same line, division is done before subtraction, which is not what you want. The final result is correct.
Differentiate with respect to x using the quotient rule?
Y= (2x^{4} – 3x) / (4x -1)
d/dx [2x^{4} – 3x] = 8x^{3} – 3
and
d/dx [4x – ] = 4
by the quotient rule
f(x) = (g(x)) / (h(x)) , f’(x) = [g^{1}(x) h(x) – g(x)h^{1}(x)] / [h(x)]^{2 }
choosing g(x) = 2x^{4} – 3x and h(x) = 4x - 1
gives
dy/dx = [(8x^{3} – 3) (4x – 1) - (2x^{4} – 3x) (4) ] / (4x – 1)^{ 2}
therefore
dy/dx = (23x^{4} – 8x^{3} – 12x + 3 – 8x^{4} + 12x) / 16x^{2} – 8x + 1
therefore
dy/dx = (24x^{4} – 8x^{3} + 3) / (16x^{2} – 8x + 1)
sorry a typo there was meant to be 32.
could I check another one please
Find the integral:
∫ (5x2 + √x- (4/x2)) dx
= (5x3/3) + (2x3/2/3) + 4/x + c
= ((5x3 + 2x3/2 ) / 3) + (4/x) + c , where c is a constant
Or
= ((5x4 + 2x5/2 + 12) / 3x )) + c , where c is a constant
Find the integral:
∫ (5x^{2} + √x- (4/x^{2})) dx
= (5x^{3}/3) + (2x^{ 3/2}/3) + 4/x + c
= ((5x^{3} + 2x ^{3/2} ) / 3) + (4/x) + c , where c is a constant
Or
= ((5x^{4} + 2x ^{5/2} + 12) / 3x )) + c , where c is a constant
In plain text, is written x^y. Also, it is important to write parentheses because is completely different from . You could check the result yourself in WoldramAlpha. Just don't overuse it and do the work by hand first if you are supposed to.