Question

Match the functions with their corresponding derivatives.

• A. $-\mathrm{cosec}\left(x\right)\times \cot \left(x\right)$
• B. $2^x\ln \left(2\right)$
• C. $-{\mathrm{cosec}}^{2}x$
• D. $5x^4$

Answer 1

$\mathrm{Derivatives}\mathrm{of}\mathrm{standard}\mathrm{functions}.f\left(x\right)=x^n,\mathrm{then}f\text{'}\left(x\right)={\mathrm{nx}}^{n-1}f\left(x\right)=\cot \left(x\right),\mathrm{then}f\text{'}\left(x\right)=-{\mathrm{cosec}}^2\left(x\right)f\left(x\right)=\mathrm{cosec}\left(x\right),\mathrm{then}f\text{'}\left(x\right)=-\mathrm{cosec}\left(x\right)\cot \left(x\right)f\left(x\right)=a^x,\mathrm{then}f\text{'}\left(x\right)=a^x\ln \left(a\right)$