Find the derivative of f(x)=x^2*e^x+x
You can split the derivative into 2 parts: dx/dy (x^2*e^x) + dx/dy (x)
For the first part you have to use the product rule, so let U=x^2 V=e^x U'=2x V'=Chain rule
V'=dx/dy(e^x)dx/dy(x)=e^x1=e^x
Returning to the product rule, f'(x)=U'V+UV' So, (2xe^x)+(x^2e^x) =x(x+2)e^x
Second part is dx/dy(x)=1
Final answer =x(x+2)e^x+1
BR
Related Maths A Level answers
All answers ▸A curve has parametric equations x= 2sin(t) , y= cos(2t) + 2sin(t) for -1/2 π≤t≤ 1/2π , show that dy/dx = - 2sin(t)+ 1
y=e^2x-11e^x+24 Find the stationary point, nature of the stationary point, the x-intercepts and the y-intercept (calculator allowed)
Differentiate ((x^2)+1)^2
What is 'e' and where does it come from?