Explanation: We have: # (sinx)^ (1/x^2)# We rewrite this as: # (sinx)^ (x^-2)# Remember this rule: #d/dx [f (x)^ (g (x))]=f (x)^ (g (x))*d/dx [ln (f (x))*g (x)]# Also ...

#lny = sqrt (cosx)ln (sinx)# Now use chain rule: #d/dx (sqrt (cosx)) = -sinx/ (2sqrt (cosx))# #d/dx (ln (sinx)) = cosx/sinx# By the product rule: # (1/y)dy/dx = -1/2sinx/sqrt (cosx)ln (sinx) + sqrt …

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Differentiate y = ex1 2? Use the limit definition of differential coefficient only. How to do question 10? How do you expand ln(24 3−1 (52))? Determine the value of x when (-1,-1)is equidistant …

Feb 9, 2018 · The answer is B For this problem I assume that log (a) = ln (a) Let's rewrite the denominator in terms of sine and cosine exclusively. secx - cosx= 1/cosx - cosx = (1 …

How do you find the integral #ln (x^2+x+1)#? What is the derivative of an absolute value? How do you differentiate #y=ln (sin^ (2) x)#? How do you determine if #3x = |y|# is an even or odd …

Explanation: We seek (a) #f' (x)#, and (b) #d/dxe^f (x)#, where # f (x) = ln ( (ex^2)/ (x-5)^7) # Part (a): Using the properties of logarithms, we can write: # f (x ...

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How to find the general solution of #x dy/dx = xy + y# ? How do you find the y ? ln (y^2-1) - ln (y+1)=ln (sinx). A triangular playground has angles with measures in the ratio 7 : 3 : 5. What is …

Jan 16, 2018 · dy/dx = (2x^lnxlnx)/x I'm pretty fond of logarithmic differentiation. We try to take the derivative of both sides: lny = ln(x^(lnx)) lny = lnxlnx Now use implicit differentiation and the …