determine-the-derivative-of-hx2x2lnxhx2x2lnleftxright-evaluate-hehprimelefterigh

Question

Determine the derivative of h(x)=2x2ln⁡(x)h(x)=$$2x^{2\ln\left(x\right)}. $$Evaluate h′$$(e)h^{\prime}$$\left(e\right).

Accepted Answer

h′(x)=8x2ln⁡(x)−1⋅ln⁡$$(x)h^{\prime}$$\left(x\right)=$$8x^{2\ln\left(x\right)-1}$$\cdot\ln\left(x\right)h′(e)=$$8eh^{\prime}$$\left(e\right)=8e^{}

Answer

h′(x)=4x2ln⁡(x)−1⋅ln⁡$$(x)h^{\prime}$$\left(x\right)=$$4x^{2\ln\left(x\right)-1}$$\cdot\ln\left(x\right)h′(e)=$$4eh^{\prime}$$\left(e\right)=4e^{}

Answer

h′(x)=4x2ln⁡(x)⋅ln⁡$$(x)h^{\prime}$$\left(x\right)=$$4x^{2\ln\left(x\right)}$$\cdot\ln\left(x\right)h′(e)=$$4e2h^{\prime}$$\left(e\right)=$$4e^2$$

Answer

h′(x)=8x2ln⁡(x)⋅ln⁡$$(x)h^{\prime}$$\left(x\right)=$$8x^{2\ln\left(x\right)}$$\cdot\ln\left(x\right)h′(e)=$$8e2h^{\prime}$$\left(e\right)=$$8e^2$$

Determine the derivative of h(x)=2x2ln(x)h(x)=2x^{2\(\ln\)\(\left\)(x\(\right\))}. Evaluate h′(e)h^{\(\prime\)}\(\left\)(e\(\right\)).