Find the derivative function y = cos x + 5x³-sin (2x-8) y = √x-5

When solving, we use the tabular values of the derivatives of the power function, trigonometric functions and complex functions.

1)

Y = cosX + 5 * X ^ 3 – Sin (2 * x – 8);

Y ‘= (CosX)’ + (5 * X ^ 3) ‘- (Sin (2 * x – 8))’ = (CosX) ‘+ (5 * X ^ 3)’ – Sin (2 * x – 8 ) ‘* (2 * x – 8)’ =

-SinX + 15 * X ^ 2 – Cos (2 * X – 8) * 2 = 15 * X ^ 2 – 2 * Cos (2 * X – 8) – SinX.

Answer: 15 * X ^ 2 – 2 * Cos (2 * X – 8) – SinX.

2)

If Y = √ (x) – 5;

Y ‘= (√ (x))’ – 5 ‘= 1/2 * √ (x).

If Y = √ (x – 5);

Y ’= (√ (x – 5))’ * (X – 5) ’= 1 / (2 * √ (x – 5)).

Answer: Y ’= 1/2 * √ (x) or 1 / (2 * √ (x – 5)).