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To differentiate a function of x and y, you must differentiate x as you would ordinarily, and then differentiate y as you would normally, but multiply the differentiated term by dy/dx. For terms with x an...

We use the chain rule. Let u(x)=exp(x), v(x)=x^1/2, w(x) = tan(x).
Then f(x) = u(v(w(x))). So by the chain rule, f'(x) = u'(v(w(x)))*(v(w(x)))'.
u'(x) = exp(x).
By the chain rule...

We can use logarithms with base 3 to solve this equation.2x+1=log₃10002x=log₃(1000)-1x=0.5(log₃(1000)-1)x=2.64

By Trapezium Rule (with 5 segments)x 0 0.2 0.4 0.6 0.8 1y 2 1.8625 1.71830 1.56981 1.41994 1.27165≈1⁄2*(0.2) [2+1.27165+ 2( 1.8625 + 1.71830 + 1.56981 + 1.41994)]≈1⁄10 *16.41283 = 1.641By Substitution/ Pa...

(2+kx)^-3 = (2^-3)(1+kx/2)^-3 = (2^-3)(1+(-3)(kx/2) + [(-3)(-4)]/2! (kx/2)² + [(-3)(-4)(-5)]/3! (kx/2)³ +... )
= 1⁄8 [1 -(3kx/...