Limits and Deri...

What is the value of \(\frac{d}{d x}\left(2 x^{4}+x^{3}+3 x^{2}\right)\) at \(x=-1\)?

If \(x=\frac{\sqrt{2}}{\theta^{\sqrt{2}}}+\frac{1}{\theta}-\theta\), then find the value of \(\frac{d x}{d \theta}\).

What is the value of \(\lim _{{x} \rightarrow \infty} \frac{{x}^{3}+3 {x}^{2}+6 {x}+5}{{x}^{3}+2 {x}+6}\)?

If \(f(x)=\sqrt[4]{-3 x^{4}-2}\), then \(f^{\prime}(x)=?\)

Find the value of \(k\) if \(\lim _{x \rightarrow 2}\left(3 x^{2}+5 x-1\right)=k\)

Find the value of \(k\) if \(\underset{{{x \rightarrow 0}}}{\lim}\frac{-3 x^{2}-7 x+8}{7 x^{2}+2 x+2}=k\)

If \(s=0.4 t^{10}+\frac{9}{t^{3}}-6 t\), then find the value of \(\frac{d s}{d t}\).

Find the value of \(\underset{{x \rightarrow 1}}{\lim} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^{2}+x-3}\)

Evaluate \(\underset{{{x \rightarrow 0}}}{\lim}\frac{\tan 2 x}{{e}^{2 x}-1}\)

If \(f(x)=\frac{\sqrt[4]{x}}{x^{-1} \sqrt{x^{5}}}\), then find the value of \(f^{\prime}(x)\).