What is the derivative of cos^2(ln(x+1)-e^{x^2}) ?

The derivative of cos^2(ln(x+1)-e^{x^2}) is -(sin(2ln(1+x)))/(1+x)-e^{x^2}*2x

What is the first derivative of cos^2(ln(x+1)-e^{x^2}) ?

The first derivative of cos^2(ln(x+1)-e^{x^2}) is -(sin(2ln(1+x)))/(1+x)-e^{x^2}*2x

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\frac{d}{d x} (cos^{2} (ln (x + 1)) - e^{x^{2}})

- \frac{sin ( 2 ln ( 1 + x ) )}{1 + x} - e^{x^{2}} \cdot 2 x

Solution steps

\frac{d}{d x} (cos^{2} (ln (x + 1)) - e^{x^{2}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (cos^{2} (ln (x + 1))) - \frac{d}{d x} (e^{x^{2}})

\frac{d}{d x} (cos^{2} (ln (x + 1))) = - \frac{sin ( 2 ln ( 1 + x ) )}{1 + x}

\frac{d}{d x} (e^{x^{2}}) = e^{x^{2}} \cdot 2 x

= - \frac{sin ( 2 ln ( 1 + x ) )}{1 + x} - e^{x^{2}} \cdot 2 x

What is the derivative of cos^2(ln(x+1)-e^{x^2}) ?
The derivative of cos^2(ln(x+1)-e^{x^2}) is -(sin(2ln(1+x)))/(1+x)-e^{x^2}*2x
What is the first derivative of cos^2(ln(x+1)-e^{x^2}) ?
The first derivative of cos^2(ln(x+1)-e^{x^2}) is -(sin(2ln(1+x)))/(1+x)-e^{x^2}*2x