How do I find the derivative of 13 14 amd 15 Review Sheet Yo

How do I find the derivative of 13, 14, amd 15

Review Sheet: You do NOT have to simplify results involving the product, quotient and chain rules. Find the derivative of each function on problems 1-15. f(x) = x^4 +2x^3 - 5x + 4 f(x) = 3x^4 + 5 + Squareroot x f(x) = 4x^3 - 6x + 3 + 3/x^2 f(x) = (4x^3 - 6x + 3)(5x^2 + 2x + l) f(x) = 3x^2 + 2/x^2 - 6x f(x) = (2x^2 + 5x)^10 f(x) = 4x^3(2x^2 + 5x)^10 f(x) = Squareroot 4x^3 - 6x + 3 f(x) = (3x^2 + 2/x^2 - 6x)^8 f(x) = e^x f(x) = ln(x) f(x) = 4e^x^2+5x f(x) = x^2e^5x f(x) = ln(5x^2 + 3x) f(x) = x^2 ln(x)

Solution

13)given f(x)=x²e^5x

differentiate with respect to x . product rule:(uv)\'=u\'v+uv\' ,d/dx xⁿ=nx^n-1 ,d/dx e^f(x)=e^f(x)*f \'(x)

f \'(x)=(x²)\'e^5x +x²(e^5x)\'

f \'(x)=(2x^2-1)e^5x +x²(e^5x*5*1)

f \'(x)=(2x)e^5x +x²(5e^5x)

f \'(x)=(2x +5x²)e^5x

14)given f(x)=ln(5x²+3x)

differentiate with respect to x .d/dx ln(f(x))=(1/f(x))*f \'(x)

f \'(x)=(1_/(5x²+3x))(5*2x +3*1)

f \'(x)=(1_/(5x²+3x))(10x +3)

f \'(x)=(10x +3)_/(5x²+3x)

15)given f(x)=x²ln(x)

differentiate with respect to x . product rule:(uv)\'=u\'v+uv\' ,d/dx xⁿ=nx^n-1

f \'(x)=(x²)\'ln(x) +x²(ln(x))\'

f \'(x)=(2x^2-1)ln(x) +x²(1/x)

f \'(x)=(2x)ln(x) +x

f \'(x)=x(2ln(x) +1)