Differentiate the following with respect to x(i) y = a/x4 - b/x2 + cos

1.	Differentiate the following with respect to x(i) y = a/x4 - b/x2 + cosx(ii) y = sin(x + a)
Answer» (i) y = ax^-4 - bx^-2 + cosx ∴ dy/dx = a(-4x^-5) - b(-2x^-3) - sinx = - 4ax^-5 + 2bx^-3 - sinx (ii) y = sinxcosa + sinacosx ∴ dy/dx = cosa. dy/dx sinx + sina d/dxcosx = cosa . cosx - sinasinx = cos(x + a)

Differentiate the following with respect to x(i) y = a/x4 - b/x2 + cosx(ii) y = sin(x + a)

Answer»

(i) y = ax^-4 - bx^-2 + cosx

∴ dy/dx = a(-4x^-5) - b(-2x^-3) - sinx

= - 4ax^-5 + 2bx^-3 - sinx

(ii) y = sinxcosa + sinacosx

∴ dy/dx = cosa. dy/dx sinx + sina d/dxcosx

= cosa . cosx - sinasinx

= cos(x + a)

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