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 ▸Differentiate cos(2x^3)/3x
a) Simplify 2ln(2x+1) - 10 = 0 b) Simplify 3^(x)*e^(4x) = e^(7)
Find the binomial expansion of (4-8x)^(-3/2) in ascending powers of x, up to and including the term in x^3. Give each coefficient as a fraction in its simplest form. For what range of x is a binomial expansion valid?
A line runs between point A(5,9) and B(11,1). Find the equation of the line. Point C lies on the line between A and B. The line with equation 2y=3x+12 also crosses through point C. Find the x coordinate of Point C.