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Popular >

derivative of cos^2(ln(x+1)-e^{x^2})

Solution

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

Solution

- \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

Popular Examples

derivative of y=5x-1 derivative of

y = 5 x - 1

integral from pi/2 to pi of 2cot(x/3)

\int_{\frac{π}{2}}^{π} 2 cot (\frac{x}{3}) d x

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x \to 1 lim (\frac{x + 1}{x ^{3} + 1})

derivative of 0.1x^3-0.45x^2+2.43x+300

\frac{d}{d x} (0.1 x^{3} - 0.45 x^{2} + 2.43 x + 300)

integral of (sin^5(x))/(cos^4(x))

\int \frac{sin ^{5} ( x )}{cos ^{4} ( x )} d x

Frequently Asked Questions (FAQ)

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