x^{x} + x^{a}+a^{x}+a^{a}, किसी नियत a>0 तथा x>0 के लिए x के सापेक्ष अवकलन कीजिए
Answers
dy/dx = xˣ ( 1 + logx) + axᵃ⁻¹ + aˣloga
Step-by-step explanation:
y = xˣ + xᵃ + aˣ + aᵃ
=> dy/dx = d(xˣ)/dx + d(xᵃ)/dx + d(aˣ)/dx + d(aᵃ)/dx
=> dy/dx = d(xˣ)/dx + axᵃ⁻¹ + d(aˣ)/dx + 0
=> dy/dx = d(xˣ)/dx + axᵃ⁻¹ + d(aˣ)/dx
d(xˣ)/dx = du/dx
u = xˣ
log u = xlogx
(1/u)(du/dx) = x/x + logx
=> du/dx = u ( 1 + logx)
=> du/dx = xˣ ( 1 + logx)
=> d(xˣ)/dx = xˣ ( 1 + logx)
d(aˣ)/dx = dv/dx
v = aˣ
logv = xloga
(1/v)dv/dx = loga
=> dv/dx = vloga
=> dv/dx = aˣloga
=> d(aˣ)/dx = aˣloga
dy/dx = d(xˣ)/dx + axᵃ⁻¹ + d(aˣ)/dx
=> dy/dx = xˣ ( 1 + logx) + axᵃ⁻¹ + aˣloga
और अधिक जानें :
(x + 3)^{2} .(x + 4)^{3} .(x + 5)^{4} प्रदत्त फलनों का x के सापेक्ष अवकलन कीजिए
brainly.in/question/15287089
f(x) = (1 + x) (1 + x^{2}) (1 + x^{4}) (1 + x^{8}) द्वारा प्रदत्त फलन का अवकलज ज्ञात कीजिए और इस प्रकार f'(1) ज्ञात कीजिए।
brainly.in/question/15287093