How do I find the derivative of 13, 14, amd 15 Review Sheet: You do NOT have to

Question

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)

Explanation / Answer

13)given f(x)=x2e5x

differentiate with respect to x . product rule:(uv)'=u'v+uv' ,d/dx xn=nxn-1 ,d/dx ef(x)=ef(x)*f '(x)

f '(x)=(x2)'e5x +x2(e5x)'

f '(x)=(2x2-1)e5x +x2(e5x*5*1)

f '(x)=(2x)e5x +x2(5e5x)

f '(x)=(2x +5x2)e5x

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=nxn-1

f '(x)=(x2)'ln(x) +x2(ln(x))'

f '(x)=(2x2-1)ln(x) +x2(1/x)

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

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

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