Похідна добутку функцій

$f^{\prime}\left(x\right)=\cos x\cdot\sin x+\sin x\cdot\cos x$

$f\left(x\right)^{\prime}=\cos x\cdot\left(-\sin x\right)+\cos x\cdot\sin x$

$f^{\prime}\left(x\right)=\cos x\cdot\cos x+\sin x\cdot\left(-\sin x\right)$

$f^{\prime}\left(x\right)=2x\cdot\sin x+x^2\cdot\cos x$

$f\left(x\right)^{\prime}=x^2\cdot\left(-\sin x\right)+x^2\cdot\cos x$

$f^{\prime}\left(x\right)=2x\cdot\cos x+x^2\cdot\left(-\sin x\right)$

$f^{\prime}\left(x\right)=\sqrt{x}+x\cdot\frac{1}{2\sqrt{x}}$

$f\left(x\right)^{\prime}=\sqrt{x}+x^2\cdot\frac{1}{\sqrt{x}}$

$f^{\prime}\left(x\right)=x\cdot\sqrt{x}+\frac{1}{2\sqrt{x}}$

$f^{\prime}\left(x\right)=\frac{1}{2\sqrt{x}}\cdot\sin x+\sqrt{x}\cdot\cos x$

$f\left(x\right)^{\prime}=\sqrt{x}\cdot\cos x+\sqrt{x}\cdot\sin x$

$f^{\prime}\left(x\right)=\frac{1}{2\sqrt{x}}\cdot\cos x+\sqrt{x}\cdot\sin x$

$f^{\prime}\left(x\right)=e^{x}\cdot2x^3+e^{x}\cdot6x^2$

$f\left(x\right)^{\prime}=e^{x}\cdot6x^2+e^{x}\cdot2x^3$

$(u ⋅ v)' = u'⋅v - u'⋅v$

$(u ⋅v)' = u'⋅v + u⋅v'$

$(u + v)' = u' - v'$

$(u + v)' = u' + v'$

$f^{\prime}\left(x\right)=e^{x}+x\cdot e^{x}$

$f\left(x\right)^{\prime}=x\cdot e^{x}+e^{x}$

$f^{\prime}\left(x\right)=e-x\cdot e^{x}$

$f^{\prime}\left(x\right)=2\cdot\tg x+2x\cdot\frac{1}{\cos^2x}$

$f\left(x\right)^{\prime}=2\cdot\tg-2x\cdot\frac{1}{\sin^2x}$