Differentiate the function (y = 4x³+ e^x + sinx)

1. Differentiate the function

y = 4x³+ e^x + sinx 

Sol: y = 4x³+ e^x + sinx 

[Note: d(x^n)/dx = nx^n-1, d(e^x)/dx = e^x,

d(sinx) /dx = cosx]

dy/dx = 4×3x³-¹ +e^x +cosx

dy/dx = 12x² +e^x +cosx.

2. Differentiate 4e^x – 5logx

Sol: 4e^x – 5logx

= d/dx ( 4e^x – 5logx)

= d/dx(4e^x) – d/dx(5logx)

= 4d/dx(e^x) – 5d/dx(loge^x)

= Ae^x– 5/x

3. Differentiate cofficient logsinx.

Sol: We have

=d/dx(logsinx)

=1/sinx d/dx(sinx)

=1/sinx (cosx)

= Cosx/sinx

= cotx

4. Find the derivatives of x⁹.

Sol:

We know that

d/dx(x^n) = nx^n-1

So, We have

d/dx(x⁹) = 9x(⁹-¹)

d/dx(x⁹) = 9x⁸.

5.Find the derivatives of x-³.

Sol:

We know that

d/dx(x^n) = nx^n-1

So, We have

d/dx(x-³) = -3x(-³-¹)

d/dx(x-³) = -3x-⁴

d/dx(x-³) = -3/x⁴.

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